This article uses the term "super-virgin birth" to represent the manner in which Catholicism and Eastern Orthodoxy go above ("super") the Biblical doctrine that Jesus Christ was born of a virgin, and teach that Mary remained physically a virgin, even after giving birth to Jesus.
This is a specific aspect of the doctrine of the perpetual virginity of Mary, in which it is taught that Mary's maidenhead remained intact, even after giving birth to Jesus Christ.
In Eastern Orthodoxy, this doctrine can be seen in the universally-accepted Synod of Jerusalem:
Synod of Jerusalem (1672 AD) - Decree 7
We believe the Son of God, Jesus Christ, to have emptied Himself, that is, to have taken into His own Person human flesh, being conceived of the Holy Spirit, in the womb of the ever-virgin Mary; and, becoming man, to have been born, without causing any pain or labor to His own Mother after the flesh, or injury to her virginity, to have suffered, to have been buried, to have risen again in glory on the third day, according to the Scriptures, to have ascended into the heavens, and to be seated at the right hand of God the Father. Whom also we look for to judge the living and the dead.
Within Catholicism, this doctrine is taught in the Second Vatican Council (1962-65 AD), and echoed in the Universal Catechism:
Vatican 2 (1965 AD) - Lumen Gentium
57 This union of the Mother with the Son in the work of salvation is made manifest from the time of Christ's virginal conception up to His death it is shown first of all when Mary, arising in haste to go to visit Elizabeth, is greeted by her as blessed because of her belief in the promise of salvation and the precursor leaped with joy in the womb of his mother. This union is manifest also at the birth of Our Lord, who did not diminish His mother's virginal integrity but sanctified it, when the Mother of God joyfully showed her firstborn Son to the shepherds and Magi.
Catechism of the Catholic Church 499
499 The deepening of faith in the virginal motherhood led the Church to confess Mary's real and perpetual virginity even in the act of giving birth to the Son of God made man. In fact, Christ's birth "did not diminish his mother's virginal integrity but sanctified it." And so the liturgy of the Church celebrates Mary as Aeiparthenos, the "Ever-virgin".
Catechism of the Catholic Church 510
510 Mary "remained a virgin in conceiving her Son, a virgin in giving birth to him, a virgin in carrying him, a virgin in nursing him at her breast, always a virgin" with her whole being she is "the handmaid of the Lord" (Luke 1:38).
Therefore, incredibly, simply being able to believe that Mary gave birth to Jesus in a normal way, where He passed through her birth canal as a child normally does, requires one to be Protestant. Both major Imperialist traditions do not allow one to believe that Jesus was born of Mary in a normal manner, instead asserting that a miracle took place that is not mentioned or implied anywhere in the text of Scripture.
Both traditions have elevated Mary to such unbiblical heights (see extensive documentation here), that they have proceeded to go beyond even a legitimate miracle God performed with Mary - the virgin birth - and in essence assert that she did not actually give birth to Jesus. A baby cannot be born of a woman without breaking her maidenhead, which is what this doctrine specifically denies. So, Jesus's body could not have passed through her birth canal. Instead, somehow, God phased the body of the Lord through it. This is unknown to Scripture, which when mentioning Jesus's birth, never indicates anything of the sort taking place (Matthew 1:25, Luke 2:7, Galatians 4:4).
The Biblical argumentation given for this doctrine is based on Isaiah 66:7:
Isaiah 66:6-13
6 A voice of noise from the city, a voice from the temple, a voice of the LORD that rendereth recompence to his enemies.
7 Before she travailed, she brought forth; before her pain came, she was delivered of a man child.
8 Who hath heard such a thing? who hath seen such things? Shall the earth be made to bring forth in one day? or shall a nation be born at once? for as soon as Zion travailed, she brought forth her children.
9 Shall I bring to the birth, and not cause to bring forth? saith the LORD: shall I cause to bring forth, and shut the womb? saith thy God.
10 Rejoice ye with Jerusalem, and be glad with her, all ye that love her: rejoice for joy with her, all ye that mourn for her:
11 That ye may suck, and be satisfied with the breasts of her consolations; that ye may milk out, and be delighted with the abundance of her glory.
12 For thus saith the LORD, Behold, I will extend peace to her like a river, and the glory of the Gentiles like a flowing stream: then shall ye suck, ye shall be borne upon her sides, and be dandled upon her knees.
13 As one whom his mother comforteth, so will I comfort you; and ye shall be comforted in Jerusalem.
Verse 7 says "before she travailed, she brought forth; before her pain came, she was delivered of a man child". This restatement of the same thing after a pause, in slightly different wording, is extremely common in poetic sections of the Bible, and this is saying that a birth took place extremely quickly. The "she" in the passage refers to "Zion" ("Jerusalem"), bringing forth "children", plural, and a "nation" (verse 8). Verse 8's mention of Zion's "travail" means that verse 7 uses hyperbole to convey the idea of a very rapid birth that is so fast, it is as if there is no time for labor pains.
So, there is "travail", "children", plural, and also what's being spoken of is Jerusalem, which Mary is never paralleled with anywhere in Scripture, and in light of verse 12 especially, refers to the city, or nation of Israel as a whole, and not a single person.
Further, in Roman Catholic thinking, this painless birth was due to Mary not inheriting Original Sin, and therefore avoiding the curse on Eve in Genesis 3:16 - "in sorrow thou shalt bring forth children". However, a woman's maidenhead breaking had absolutely nothing to do with the curse in the Garden of Eden, as all women before the fall still would have given birth through their birth canal, which would have broken their maidenhead if it were somehow still intact after conceiving. This doctrine goes beyond a woman merely giving birth without labor pains, which is the type of "pain" specifically being spoken of in Isaiah 66:7. But, even granting that this passage applies to Mary (which it does not), and meant that Mary had no pain anywhere in her body whatsoever when giving birth to Jesus (which is not what it refers to), God could easily have made Mary's maidenhead breaking painless. This passage, even if all concessions are granted, does not get one to a super-virgin birth.
Finally, recognize that due to the dearth of Biblical support for the Marian obsession displayed by Catholicism and Orthodoxy, it seems that any verse mentioning a woman giving birth can be applied to Mary, even if context disallows it. Here, in Isaiah 66:7, the woman allegedly has no travail. In Revelation 12:1-2, there is a woman "travailing in birth, and pained to be delivered", yet this too is endlessly applied to Mary in Catholicism (Pope Pius X, Ad Diem Illum Laetissimum #24, Pope Pius XII, Munificentissimus Deus #27, etc.). Although neither passage in context can refer to Mary, and the woman in one passage allegedly has no travail, while the other has travail, still it is asserted that both passages apply to Mary, because context does not actually matter so long as Mary can be exalted by the application of the passage to her.
The Protoevangelium of James is considered the primary source of this doctrine, which later generations would attempt to read back into Scripture, as discussed above. This text, which is also responsible for Eastern Orthodoxy's doctrine that Mary lived in the Holy of Holies, is known to be early, as Origen (185-253 AD) refers to a version of it.
In the text, Salome does not believe that Mary has given birth as a virgin, and, being made to plagiarize - or rather, blasphemously parody - doubting Thomas (John 20:25-27), says that she will not believe unless she examines Mary herself:
Protoevangelium of James, Chapter 19-20
19 It is Mary that was reared in the temple of the Lord, and I obtained her by lot as my wife. And yet she is not my wife, but has conceived of the Holy Spirit. And the midwife said to him: Is this true? And Joseph said to her: Come and see. And the midwife went away with him. And they stood in the place of the cave, and behold a luminous cloud overshadowed the cave. And the midwife said: My soul has been magnified this day, because my eyes have seen strange things - because salvation has been brought forth to Israel. And immediately the cloud disappeared out of the cave, and a great light shone in the cave, so that the eyes could not bear it. And in a little that light gradually decreased, until the infant appeared, and went and took the breast from His mother Mary. And the midwife cried out, and said: This is a great day to me, because I have seen this strange sight.
And the midwife went forth out of the cave, and Salome met her. And she said to her: Salome, Salome, I have a strange sight to relate to you: a virgin has brought forth - a thing which her nature admits not of. Then said Salome: As the Lord my God lives, unless I thrust in my finger, and search the parts, I will not believe that a virgin has brought forth.
20 And the midwife went in, and said to Mary: Show yourself; for no small controversy has arisen about you. And Salome put in her finger, and cried out, and said: Woe is me for mine iniquity and mine unbelief, because I have tempted the living God; and, behold, my hand is dropping off as if burned with fire.
In addition to the Protoevangelium of James, this doctrine is also thought to have been influenced by an account in the Ascension of Isaiah, which is a text dated variously to the first or second century AD.
In it, Jesus simply appears outside of Mary, without any birth process whatsoever taking place, when she and Joseph are at home one day:
The Ascension of Isaiah 11:5-14
5 And he did not approach May, but kept her as a holy virgin, though with child.
6 And he did not live with her for two months.
7 And after two months of days while Joseph was in his house, and Mary his wife, but both alone.
8 It came to pass that when they were alone that Mary straight-way looked with her eyes and saw a small babe, and she was astonished.
9 And after she had been astonished, her womb was found as formerly before she had conceived.
10 And when her husband Joseph said unto her: "What has astonished thee?" his eyes were opened and he saw the infant and praised God, because into his portion God had come.
11 And a voice came to them: "Tell this vision to no one."
12 And the story regarding the infant was noised broad in Bethlehem.
13 Some said: "The Virgin Mary hath borne a child, before she was married two months."
14 And many said: "She has not borne a child, nor has a midwife gone up (to her), nor have we heard the cries of (labour) pains." And they were all blinded respecting Him and they all knew regarding Him, though they knew not whence He was.
To note a few things on these two sources:
Finally, the Odes of Solomon, a text dated to first or second century AD, contains a passage that alludes to a painless birth of the Messiah, couched within some truly bizarre statements:
The Odes of Solomon - Ode 19
1 A cup of milk was offered to me: and I drank it in the sweetness of the delight of the Lord.
2 The Son is the cup and He who was milked is the Father:
3 And the Holy Spirit milked Him: because His breasts were full, and it was necessary for Him that His milk should be sufficiently released;
4 And the Holy Spirit opened His bosom and mingled the milk from the two breasts of the Father and gave the mixture to the world without their knowing:
5 And they who receive in its fulness are the ones on the right hand.
6 The Spirit opened the womb of the Virgin and she received conception and brought forth; and the Virgin became a Mother with many mercies;
7 And she travailed and brought forth a Son, without incurring pain;
8 And because she was not sufficiently prepared, and she had not sought a midwife (for He brought her to bear) she brought forth, as if she were a man, of her own will;
9 And she brought Him forth openly, and acquired Him with great dignity,
10 And loved Him in His swaddling clothes and guarded Him kindly, and showed Him in Majesty. Hallelujah.
The above is a strange, potentially heterodox description of the Father being "milked" by the Holy Spirit. Verse 8 says that "she brought forth, as if she were a man, of her own will", which makes it sound as if she had direct agency over when she gave birth, making it odd that she would have chosen to have done so in a crowded Bethlehem while her and Joseph were without accommodation, and away from home.
Yet, because this doctrine has no Scriptural warrant at all, texts like the above are all that proponents of it have to work from. Of course, they employ the same tactics that Muslims employ when attempting to defend the pseudepigraphal narratives that found their way into the Quran, by saying that these documents, though heretical, represent a genuine tradition in the parts which they need to affirm. This ad-hoc excuse is unfalsifiable, and can be used to justify believing literally anything from any forged document in history.
And, to reiterate, even if one were to grant that Mary had an entirely painless birth, there is no reason to believe that Mary's maidenhead remained intact, as God could have made her maidenhead breaking painless, just as He would have made everything else associated with the birth that typically causes pain painless as well. A mere statement that the birth was painless, as in the Odes of Solomon, does not count as evidence. One would need something like in the Protoevangelium of James, or the Ascension of Isaiah, wherein Mary did not actually give birth to Jesus through her birth canal, in order to support the super-virgin birth.
The unbiblical doctrine of the super-virgin birth appears to have stemmed from forged, heterodox writings which were designed to exalt Mary for whatever purposes the writer devised, long after the ones in whose names they were writing had already passed away. Yet, it is a doctrine bound infallibly on the conscience of Christians by the Roman Catholic and Eastern Orthodox Churches.