Both.

Matthew gives the lineage of Yahshua through his only earthly parent, Miriam, through the lineage of King David by way of his son Solomon.  In verse 16 in most translations of the Bible, Joseph is listed as the husband of Mary, which makes Yahshua the 13^th generation from the “carrying away into Babylon unto Messiah” enumerated in verse 17, and thus causes a fatal error in the enumeration of his geneaology which clearly states that he was the 14^th generation.

Our modern translations come from the Greek version of Matthew.  Matthew was not written in Greek.  According to several first and second century sources, Matthew was well-known to have been written in the Hebrew language.  From Hebrew, it was translated into the more common Aramaic language, and from Aramaic it was eventually translated into Greek.  That is why many Aramaic words still remain in the Greek text and are even transmitted over into the English translations of Matthew.  The word “husband” in verse 16 is the Greek word “aner” which broadly means, “a man of full age,” and can be translated as “man,” “father,” “husband,” or any adult male.  However, the Aramaic word that was translated “aner,” is givra, which literally means “mighty man” and is commonly used to refer to the oldest man in the family clan, most appropriately translated “father.”  Thus, Miriam’s father (givra) was the son of Yosef, who was the son of Ya’acov.

Verse 19 indicates that another man named Yosef was her “ba-ala” (Aramaic for husband). This becomes very clear when we compare the genealogy of her husband Yosef which is detailed in Luke 3:23 and following.  Miriam’s husband Yosef was commonly supposed to be the father of Yahshua, but this man Yosef was the son of Heli, which was the son of Matthat, whose lineage goes back to King David as well, but through David’s son Nathan, who was not of the king line (Luke 3:31).  The Yosef whose lineage is detailed in Luke 3 is Miriam’s husband of Matthew 1:19 and was Yahshua’s stepfather - only a distant relative of Yahshua through his only earthly parent Miriam.