And I should add that it's not just a question of possible divorce.
There is also the risk of one party one day needing to declare bankruptcy, often because of unbearably high medical bills that aren't covered by insurance for one reason or another. The home (= jointly held mortgage) would be protected, and if all other forms of credit are held separately, the non-BK partner's credit would remain intact. They could continue to function with that partner's credit, and when it came time for the BK party to rebuild, s/he could go AU on the other's cards, thus recovering much more quickly.
But besides the general concerns, I think that OP's scenario of both parties having baddies might well make chances for approval even worse, by doubling the negatives in a sense.
* Credit is a wonderful servant, but a terrible master. * Who's the boss --you or your credit?
FICO's: EQ 781 - TU 793 - EX 779 (from PSECU) - Done credit hunting; having fun with credit gardening. - EQ 590 on 5/14/2007