Dear Joseph:

It is thought that the genealogy in Luke 3:23-38 is that of Mary and the genealogy of Mt 1:1-17 is that of St. Joseph. There is little support for this theory. St. Thomas Aquinas, following St. Augustine on this point, suggests that the St.Matthew's account stresses the messianic character of our Lord; and St. Luke's account teaching us about His priesthood. (see St. Thomas Aquinas, Summa theologiae, III, q. 31, a. 3 ad 3).

For more detail on this see the commentary on Luke 3:23-28 in the Navarre Bible: The Gospel of St. Luke

There is Biblical evidence, however, in the words of St. Paul in Romans 1:3 when he affirms that Jesus "was descended from David according to the flesh" (RSV-CE). The Douay-Rheims translation may make even more clear when it says that Jesus  was "of the seed of David, according to the flesh"

Since Jesus was not of the seed of St. Joseph how could He descended from "David according to the flesh"? St. Joseph gave Jesus the legal status as a descendent of David, not that which is "according to the flesh."

Thus the only way that Jesus could be "of the seed of David" is for Mary to have been of the line of David also.

In addition, there appears to be direct inspired testimony of Mary as a descendant of David. In Luke 1:26-27 we read "in the sixth month the angel Gabriel was sent from God. . .to a virgin espoused to a man whose name was Joseph, of the house of David". Reading this text with the mindset of English grammar might and does cause people to interpret this as referring to Joseph as being "of the house of David." This is not true, however. The clause "of the house of David" refers to the virgin who is the principal person in the narrative. This interpretation of this passage is affirmed by the Church Fathers (Cf. St. Ignatius., ad Ephes, 187; St. Justin, c. Taryph., 100; St. Augustine, c. Faust, xxiii, 5-9)

As Catholics, of course, we know that not everything is in the Bible, nor has to be in the Bible. The Bible itself says that not everything is recorded in the Gospels (Jn 21:25). While genealogy of Mary is Biblically implied by St. Paul and St. Luke appears to write the inspired knowledge that Mary was of the Line of David, this notion is further confirmed by both theological logic and by the teaching of the Fathers of the Church.

The theological logic stems from the words of St. Paul. It is about the legal and blood lines that would be required for Jesus to be the Messiah. Jesus had to come from the Line of David. Since Joseph was not his father Jesus could not have been in the blood-line of David. He qualifies as Messiah by having the blood-line of David through Mary.

It was also required according to the Jewish economy that the Messiah not only be of the blood-line of David, but legally of David's line. St. Joseph, as foster father, provides that legal link.

The Church Fathers (see the saints mentioned above who commented on the Lukian passage, and others) and Church Tradition affirm all this.

God Bless,
Bro. Ignatius Mary