The genealogy written in Matthew chapter 1 is Joseph’s side, husband of Mary. Luke 3:23 is referencing Mary’s, mother of Jesus, lineage. It was customary to list the lineage through males, so Mary’s name was omitted and replaced with Joseph. Heli was father to Mary, father-in-law of Joseph.

Part of an article from 2017 Matthew’s account about the events related to Jesus’ birth and early life differs somewhat from Luke’s account because the Gospel writers told the events from different perspectives. Matthew’s account focuses on events that involved Joseph. It relates Joseph’s initial reaction to Mary’s pregnancy, his dream in which an angel explained the situation, and the acceptance of that explanation. (Matt. 1:19-25) Matthew goes on to tell about Joseph’s dream in which an angel urged him to flee to Egypt, his flight with his family, his dream in which an angel told him to return to the land of Israel, his return, and his decision to settle his family in Nazareth. (Matt. 2:13, 14, 19-23) In the opening chapters of Matthew’s Gospel, Joseph’s name is mentioned eight times, but Mary’s, only four. On the other hand, Luke’s account is much more focused on Mary. It includes Mary’s being visited by the angel Gabriel, her visit to her relative Elizabeth, and Mary’s expression of praise to Jehovah. (Luke 1:26-56) Luke also mentions Simeon’s words to Mary regarding Jesus’ future sufferings. Even in the account of her family’s visit to the temple when Jesus was 12 years old, Luke quotes the words of Mary, not those of Joseph. Luke adds that Mary was deeply affected by all these events. (Luke 2:19, 34, 35, 48, 51) In the first two chapters of Luke’s Gospel, Mary’s name is mentioned 12 times, but Joseph’s, only 3. So, then, Matthew describes more of Joseph’s concerns and activities while Luke gives more details about Mary’s role and experiences. Likewise, the genealogies supplied by the two Gospel writers differ. Matthew traces Joseph’s ancestry and shows that Jesus as Joseph’s adopted son was the legal heir to David’s kingship. Why? Because Joseph was a descendant of King David through the line of David’s son Solomon. (Matt. 1:6, 16) However, Luke evidently traces Mary’s ancestry and shows that Jesus was the natural heir, “according to the flesh,” to David’s kingship. (Rom. 1:3) Why? Because Mary was a descendant of King David through the line of David’s son Nathan. (Luke 3:31) But why does Luke not list Mary in his genealogy as the daughter of Heli, her father? Because official genealogies were generally traced through the men. So when Luke lists Joseph and describes him as the son of Heli, it was understood to mean that Joseph was Heli’s son-in-law.—Luke 3:23. The genealogical lists by Matthew and Luke clearly establish that Jesus was the foretold Messiah. In fact, the truth about Jesus’ genealogy was so well-known that even the Pharisees and Sadducees could not deny it. Today, both Matthew’s and Luke’s genealogical records remain a part of the foundation of our faith and a testimony to the sureness of the promises of God.