I've been dying to know the correct answer. Never know which to use in my thesis.
Here's an example:
The tree whose leaves were falling died.
The tree which leaves were falling died.
I don't object to "whose" either but if you felt odd about it: The tree that was losing its leaves died.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
Whose is fine to me.
I'll go "whose" too if you're dividing up the cheque. (But I think the answer is over-valued).