I am duly disagreed with! ;-)
OK, having read Barb and 5jj's posts, I will say that I retract my rather emphatic "No!" from my first post.
Yes, it is possible to say "Tom and Linda's father" and that is probably what is said more often than not.
However, I would like to know if Barb really doesn't agree that that could be ambiguous when spoken.
For example (in writing):
- Who did you buy the farm from?
- From Tom, and Linda's father.
That's clear that it's two separate people. Without the comma in the written version, I too would assume that they were siblings and the farm was bought from one man, their father.
When spoken, with no pause for the comma:
- Who did you buy the farm from?
- From Tom and Linda's father.
Do you know for sure that s/he bought the farm from the father of two siblings called Tom and Linda, or would you entertain the possibility that s/he bought it from Linda's father and from Tom, who were co-owners of the farm?
It should also be noted that "Tom and Linda's father" as quoted in the original post is not a complete sentence, nor was the OP's alternative suggestion. Of course, on top of that, there is the fact that the context of the conversation/article and the rest of the sentence might make it entirely clear which one we mean.