There are several questions raised by your inquiry, so as always, I would recommend trying to consult with an attorney. However, based on the information you've provided, a credit card company would not have any basis to go after your husband if he did not agree to pay. Since you say only you signed the agreement for the card, you should be the only one on the hook.
With that said, if you and your husband have a joint checking account, the creditor may be able to hit that, but most courts in ohio will recognize your husband's separate income as exempt (there are a few that may not though, and could hold that 50% of those funds belong to you by law).
If you have no income, the credit card co. cannot garnish your wages (since you have none).