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.
Sorry wrong tribe ; He is of the house of David as King
and High Priest under the order of Melchizedek
Ge. 14:18 Then Melchizedek king of Salem [That is, Jerusalem] brought out bread and wine. He was priest of God Most High,
and Hebrew 5 through 7.
b'shem Y'shua