Typically you are only responsible for the debts of your spouse if he or she dies. I liked this post in the Wills, Trusts & Estate blog regarding what you should know, and do, if you have a relative (parent, usually) who dies with debt: http://lawprofessors.typepad.com/trusts_estates_prof/2010/09/what-to-do-when-your-relative-dies-with-debt.html.
