Actually, Mary did concieve without sex (I'm Catholic, FYI) Here's a link:
The angel to remove Mary's anxiety and to assure her that her virginity
would be spared, answered: "The Holy Ghost shall come upon thee and the power of the Most High shall overshadow thee. And therefore also the Holy which shall be born of thee shall be called the Son of God." In token of the truth of his word he made known to her the conception of St. John, the miraculous pregnancy of her relative now old and sterile: "And behold, thy cousin Elizabeth; she also has conceived a son in herold age, and this is the sixth month with her that is called barren: because no word shall be impossible with God." Mary may not yet have fully understood the meaning of the heavenly message and how the maternity might be reconciled with her vow of virginity
, but clinging to the first words of the angel and trusting to the Omnipotence of God she said: "Behold the handmaid of the Lord, be it done to me according to thy word."http://www.newadvent.org/cathen/01541c.htm
That was in the explination of the Annunciation (when the angel Gabriel told Mary that she would concieve)
It's even in our Creed. Jesus Christ ".....was born of the Virgin Mary" is part of what we say at every Mass. So it's believed by every Catholic that adheres to the Church's teachings.
And the difference between the Anglican/Episcopalians and Catholics is mainly fidelity to the Pope. Different doctrinal issues have come up since the split, but the original issue was the Pope's authority.