If you are on the Property Tax Listing as a owner; you both will be responsible for the back taxes, even if it goes into foreclosure. City/County possibly will go after you, your husband, and the bank. Just keep in mind that they have the authority to garnish wages and take money out of bank accounts, etc. The back taxes were due when the owners of the home (you [if you are listed as a owner] and your husband [if he is listed as owner]) owned it. It will continue to be a lien on your home for these back taxes also. They can take your home also for not paying the taxes, or would be in line with any other creditors.
Another thing you need to check on if you owned the home at the time of divorce. Often if the home is given to you in the property distribution; a quit claim deed is done for your ex to you, relinquishing their part of the ownership to the property to you (their ex spouse). That does not mean they are not responsible for the mortgage owed, etc. It just means from that day forward that the quit claim deed is filed, the spouse that it was given to is responsible for all monies owed from that day forward. So, if one was done and your name only was placed on the property, you would be responsible for all taxes owed singly once only your name is listed as sole owner.
I will be praying for you. I wish you well. I feel you and yours.