Can your husband who has bad credit co-sign a loan for his daughter your step-daughter against your will you have good credit and don't want to be responsible for this debt?

Well, either your husband has better credit than you think or he will be denied as a co-signer. The very purpose of using a co-signer is so that someone with questionable credit is supported by a financially stable person who can assume the debt should the primary borrower fail to pay it. That said, if your husband was able to co-sign a loan, the only way you could be held responsible for it is if you live in a state where the law dictates that debts between married people are shared debts.