If you are a joint account holder on your husband's credit cards, you will likely be responsible for the debts on those credit cards. As a joint account holder, you share full responsibility for the debt under the terms of the contract, even if you didn't make the charges. If you are not a joint holder on the accounts, you may not be responsible for those debts.
Some states have community property laws, sometimes called joint property laws, that make any debt incurred on credit accounts opened during marriage automatically considered joint debts. In that case, you may be responsible for any debt that your deceased spouse incurred.
Check with your lender to see if you are a joint account holder on the credit cards and then consult with an attorney to determine which accounts you may be responsible for paying. Your state's attorney general's office may also be able to provide more information about any applicable community property laws.
If you haven't already, you can request a copy of your deceased husband's credit report to have a record of his accounts and to check whether an indicator has been added to his file showing that he is deceased. Married couples do not have combined credit reports, so it's a good idea to request your credit report as well. That way, you can review your information and ensure that everything looks correct.
You can request your free credit report from each of the three credit reporting agencies at AnnualCreditReport.com. You can also view your free Experian credit report at any time here.