[audax]

Jesus would have had Mary's DNA, and not Joseph's. Joseph was of the line of David -- there is no evidence that Mary was. In fact, there is some evidence that Mary came from a Levitical family. Her sister was married to a priest.

The genealogy in Luke 3 would seem to be of Joseph's bloodline, while that in Matthew 1 records in chronological order those who inherited the royal office (passing, for example, from uncle to nephew when the uncle was without heirs).

[Uri’el-2012]

Jesus would have had Mary's DNA, and not Joseph's. Joseph was of the line of David -- there is no evidence that Mary was. In fact, there is some evidence that Mary came from a Levitical family. Her sister was married to a priest.
The genealogy in Luke 3 would seem to be of Joseph's bloodline, while that in Matthew 1 records in chronological order those who inherited the royal office (passing, for example, from uncle to nephew when the uncle was without heirs).

What you are searching for is the exception for women:
Zelophehad’s daughters

Numbers 26 & 36.

Which would imply that Miriam was of the house of David.

b'shem Y'shua

[Ohioan from Florida]

Correct. The biblical accounts of Matthew and Luke show that Jesus fit the "legal" definition of the House of David, but biologically speaking, His line came from His Mother, Mary, who was the daughter of Anna and Joachim. It has been a few years since I looked into this, but I recall that through Mary's lineage, Jesus has a Levitical heritage as well.

[SirJohnBarleycorn]

In fact, there is some evidence that Mary came from a Levitical family. Her sister was married to a priest.

Yes, there is evidence Mary was descended from Levi.

Luke 1:5 states that Mary's relative Elizabeth, was "of the daughters of Aaron." Elizabeth's husband Zacharias was a priest.