possessives - Is it correct to say "a friend of X and mine" if both X and I know each other and the friend?

As I understand it, if X and Y independently have the same friend Z, we should write

Z is a friend of X's and Y's

but if X and Y collectively have Z as a friend (e.g., X and Y are a couple), then we should indicate that by making the possessive "'s" refer to "X and Y" collectively:

Z is a friend of X and Y's

But if Y is me, how do I write the latter? I think the answer is

Z is a friend of X and mine

but it sounds awkward to me (maybe because the possessive in "mine" sounds like it only refers to me, not to X and me). It sounds better to my ear to write

Z is a friend of X's and mine

but this loses the subtlety that X and I collectively have Z as a friend.