The language of Luke 3 definitely reads as Joseph's genealogy, both in the Greek and in every English translation.
There is a widespread belief that there was a Jewish custom of substituting a woman's husband's name for hers when creating a genealogy for a woman. Thus, goes the argument, the reference to "Joseph" actually should be read as a reference to "Mary." I have several problems with this explanation:
(1) It wouldn't be a useful genealogy because nobody would know whose genealogy it even is. What would be the point of making a geneaology of woman if you are not allowed to mention the woman whose geneaology it is?
(2) Why is the author of Luke familiar with this supposedly Jewish tradition while the author of Matthew is not? Indeed, tradition holds, and their respective texts tend to support, that Luke was writing for a more gentile audience while Matthew's gospel was written for more "Jewish" Christians.
(3) Luke 1:36 says that Mary is Elizabeth's relative and Elizabeth, according to Luke 1:5 is descended from Aaron, which would make her a descendent of the tribe of Levi rather than the tribe of Judah (which is David's tribe). Not definitive certainly, but curious.
(4) Another curiousity: In verse 1:27, the author of Luke specifically points out that Joseph is a descendent of David but says nothing about Mary.
(5) Nobody seems to cite a non-apologetic source for this notion that Jewish genealogies of the time would not list women's names, even if only to identify the genealogy as that of a woman.
It's getting curiouser and curiouser . . .