Grammar girl has an explanation [1] of the rule I've heard elsewhere and always followed---splitting it into "Jack's and Jill's" if they have separate and distinct things (so "Jack's and Jill's stories") and attaching the possessive to the compound entity if they share the item (so "Jack and Jill's story"). So in this case you're definitely correct about not splitting up the possession.

I haven't been able to find anything authoritative to explain what to do when there is a pronoun involved, though I believe the correct form would be "my wife and my..." and not "my wife and I's".

[1] http://grammar.quickanddirtytips.com/grammar-compound-posses...