Hello and thank you for allowing me to address your legal question.
Unfortunately, based on what you wrote you are responsible for the mortgage, and therefore, your credit will be damaged if your husband stops paying the mortgage. In addition, depending on where the house is located, the lender may go after you for the deficiency if the loan is not paid off after the foreclosure sale (i.e. if $200,000 is owed under the mortgage, and the house sells for $150,000 at the foreclosure auction, then you may be responsible for the other $50,000). State laws vary with regard to deficiencies.
Did a judge order your husband to put the mortgage in his name? If so, then take this matter before the judge and ask that your husband be found in contempt. That may spur your husband into action. Unfortunately, if your husband is truly facing bankruptcy, then it is doubtful that a lender would take the risk of refinancing the house, particularly for the purpose of removing an obligor (i.e. removing you from the mortgage makes it even riskier for the lender since that is one less person to go after if the mortgage isn’t paid).
Your best bet is to work with your husband to pay the mortgage or sell the house. I assume the house is worth less than what is owed under the mortgage (otherwise, just sell it and avoid foreclosure!), but you may be able to avoid foreclosure by notifying the lender of your troubles, and asking for a reduced interest rate or for approval for a “short sale.” A shore sale occurs when the lender agrees to accept less than what is owed under the mortgage, thereby allowing a sale (ordinarily, a sale would be prohibited unless the lender is paid in full).
I know that’s not what you wanted to read, but I hope my answer was helpful. If so, then please remember to ACCEPT my post as that is the only way I will receive credit and compensation for my answer. Thank you and good luck!
DISCLAIMER: Please understand that the complexities of most legal problems cannot be sufficiently addressed in this setting. Accordingly, my post is intended as general information only, and should neither be construed as specific legal advice, nor as an adequate substitute for the retention of legal counsel.