I am sorry to hear of your many difficulties, financial and otherwise. Bankruptcy was designed to help people in your very situation.
You can file for Chapter 7 bankruptcy without your husband. Although both spouses can file a joint petition, they are not required to do so.
It does sound like you qualify for Chapter 7. However, you should consult with an experienced bankruptcy attorney in your home state to discuss this further.
For more information about bankruptcy issues, please check out my bankruptcy blog:
Just a caveat to add: while you CAN file by yourself, if the debt is incurred during the term of the marriage, some creditors may go after your husband anyway. It's clear from your question above that you incurred marital debt (regardless of whether the card is in your name only). So please consult with a bankruptcy attorney or two to consider the likelihood of creditors going after your husband in such an instance. If highly likely, then you may negatively impact your husband's credit in either case and a joint bankruptcy may, in fact, be your best option.
Yes, you can file for bankruptcy in your name only. However any jointly owed debts will likely shift 100% to your husband, and any jointly owned assets that are not exempt may be subject to forfeit to the bankruptcy court, at least to the extent of your ownership. As for the mortgage you can affirm the debt and keep payments going on your house just like nothing happened.