The Virgin Mary's parents are Saint Anne and Saint Joachim.

Having read the Christmas Story over again. A good student of Theology could make the case for Zechariah and Elizabeth being the parents of Mary. Scripture states, Elizabeth was a relative of Mary, and she was well into years when John the Baptist was born. No one really knows, we do know Joseph was the rightful heir to King Herod's thrown, and Mary represents the claim of Jesus to the High Priest's office as well.

(Ma′ry) [from the Heb. Miriam, possibly meaning “Rebellious”]. There are six Marys mentioned in the Bible. 1. Mary the mother of Jesus. She was the daughter of Heli, though the genealogy given by Luke lists Mary’s husband Joseph as the “son of Heli.” Says M’Clintock and Strong’s Cyclopaedia (1881, Vol. III, p. 774): “In constructing their genealogical tables, it is well known that the Jews reckoned wholly by males, rejecting, where the blood of the grandfather passed to the grandson through a daughter, the name of the daughter herself, and counting that daughter’s husband for the son of the maternal grandfather (Numb. xxvi, 33; xxvii, 4-7).” It is undoubtedly for this reason the historian Luke says that Joseph was the “son of Heli.”—Lu 3:23. Mary was of the tribe of Judah and a descendant of David. Hence it could be said of her son Jesus that he “sprang from the seed of David according to the flesh.” (Ro 1:3) Through his adoptive father Joseph, a descendant of David, Jesus had a legal right to David’s throne, and through his mother, as the “offspring,” “seed,” and “root” of David, he held the natural hereditary right to “the throne of David his father.”—Mt 1:1-16; Lu 1:32; Ac 13:22, 23; 2Ti 2:8; Re 5:5; 22:16. If tradition is correct, Heli’s wife, the mother of Mary, was Anna, whose sister had a daughter named Elizabeth, the mother of John the Baptizer. This tradition would make Elizabeth the cousin of Mary. That Mary was related to Elizabeth, who was “from the daughters of Aaron” of the tribe of Levi, the Scriptures themselves state. (Lu 1:5, 36) Mary’s sister, some have thought, was Salome, the wife of Zebedee, whose two sons, James and John, were numbered among Jesus’ apostles.—Mt 27:55, 56; Mr 15:40; 16:1; Joh 19:25.