Here's the explanation straight from "Answers to Tough Questions Skeptics ask about the Christian Faith" (long title, huh?) by Josh McDowell, same guy who wrote the book Sosiqui mentioned in her first post.

He does indeed say that Matthew traces the geneology through Joseph, while Luke traces it through Mary. "The usual practice of a Jewish geneology is to give the name of the father, grandfather, etc, of the person in view. Luke follows this pattern, and does not mention the name of Mary, but the name of the legal father (Joseph). However, Luke is quick to add that Joseph is not, in reality, the father of Jesus, since Jesus had been virgin born."

He goes on to give a literal translation of Luke 3:23- "Jesus, when He began, was about thirty years old, being the son of Joseph, as it was thought, of Heli..." He seems to think that Luke mentioned Joseph, since he was Jesus' legal father, but then skips over to Mary's family line, since that's who He's actually related to.

The final paragraph of the chapter: " The purpose of the two geneologies is to demonstrate that Jesus was in the complete sense a descendant of David. Through His foster father, Joseph, he inherited by law the royal line, while through his mother he was a flesh and blood descendant of king David."

~Mina "make sense? even a little?" moon