First let me say I am not an attorney but I have worked in the legal arena for many years, mainly on the real estate side of it.
A few questions:
Are all of the children fathered by your husband and mothered by you? In other words, no children from a prior relationship.
Why don't you know your husband's financial situation. You have been married for 20 years. Do you sign the annual IRS filings?
How long ago were your credit problems?
If your husband is the primary breadwinner, your credit does not really factor in that much. Most of the interest rate will go off of his credit rating, not yours, so you could be listed on the deed and just about anything else. The only problem would be if there were a lien against you.
The problem with the home being in his name alone is that he can sell it, mortgage it or whatever else he wants without you having any say in it. Your only protection would be if you filed for divorce before he did do something so the court could keep him from doing this, but he can still have a mortgage with a family member/friend or whomever placed in county records which may or may not be a real mortgage but would have to be taken into consideration with the divorce division of property. So see, you could end up having to pay for a mortgage that the money would essentially go back to your husband.
If you can answer my questions, then maybe I can help you more. You may call me if you like ###-###-####.