If the debt was acquired during the marriage, it is marital debt and can be allocated to either party by the divorce Judge. However, its never that simple and anyone answering would need more information before they could give an opinion either way.
For informational purposes only. Not legal advice.
There are several avenues by which you can be held liable for a debt in your spouse's name. First, if the debt was incurred during the divorce, it should be treated as a marital debt. Technically, the divorce laws (specifically 750 ILCS 5/503) address the division of property, not debt. But generally it has been commonly accepted that debt is a negative property and therefore just as divisible. So, in the divorce, the judge could order either spouse to pay the debt regardless of whose name it is in and who incurred it.
The divorce judgment, however, does not bind credit card companies and lenders. That means that even if the judge orders spouse a to pay spouse b's credit card, the credit card company will still come after spouse b. Generally, even when married a lender cannot collect from a spouse. Jointly owned assets, however, can be levied on to collect. In addition, if the debt was incurred for certain expenses, the creditor can come after the spouse under the Family Expense Act.
As with all other cases, your question does not include many of the specifics necessary to give you complete advice. You should contact an attorney if you are in or will be involved in a divorce involving debts.
With certain exceptions, credit card debit incurred during the marriage is marital debts. There is always the argument of dissipation if it applies to your case. You should discuss this with your attorney.