If my separated spouse files for personal bankruptcy and the mortgage and car loan are in both names, what happens?

You can be dragged in and will be dragged into this because there is an automatic stay that occurs on all debts. The lenders will need to seek a lift of the stay and you can have your say in what can or should happen. This is a homestead right issue, as well. If you are on the loan, you may become a creditor or a claimant depending on how this all pans out. Talk to the trustee. What outcome you wish will dictate how you go about talking with the right people. Try refinancing in your name so that she quitclaims it to you, and the lender gets a lift of the stay. If this happens, those items will no longer be a part of the bankruptcy.