Are my husband’s credit card bills my responsibility even though I didn’t know about it?

Any liability or debt that is incurred during the marriage is presumed to be a marital debt and as such, it is a joint debt. It is irrelevant if one spouse is listed on the debt and the other is not. If the debt was incurred for marital expenses, like vacations, food, clothing etc, then that debt is marital. A debt that is incurred for instance to further a relationship with someone else, is not a marital debt. Keep in mind that even though the debt is marital, the creditor cannot sue the spouse that is not listed on the application. There are things like hospital bills. They operate the same way.