My husband and I have a realty and mortgage business and we've collectively been in the business for 35 years. We have totally separate credit files, mainly for business purposes. However, we file joint married taxes. The two are completely separate. Any property you purchase in TX is community property. We both have properties (both the one we live in and investment), financed separately, yet we both still own them because we're married. Oh, and you CAN have joint bank accounts - that has nothing to do with it.
In regards to your credit. You can hire a credit repair company for their assistance, or you can talk to a qualified mortgage professional who can offer you free tips, and then do the leg-work yourself. (Because there are so many issues that I could potentially address, I can't really offer any specific advice on this venue.) If you are self-employed, there is a high probability that you will not be on the loan anyway, especially with challenged credit.
The way you keep his credit clear of your mishaps, don't add him as an authorized user on any of your active cards. He can add you to his, which in time, will begin to raise your scores as you clean up past issues. And, it goes without saying, don't apply for joint credit (car loans, instant credit, mortgages, etc.) because your scores and lack of provable income could negatively affect the terms you receive.
BTW - I've looked at the responses below mine, many of you are incorrect. Bad credit CAN and will prevent someone from getting a mortgage loan. The days of qualifying if you can fog a mirror are over, for now - watch the financial news. Unless you are applying for an FHA loan, your credit and income can be left off of the loan, as long as your husband can qualify independently. FHA is different for many reasons. Also, the 7 year rule DOES NOT APPLY. It sounds like a great idea, but those debts are sold from 1 collector to the next and will keep popping up until they are settled or successfully removed. Until then, they will show as outstanding on your report. When you are disputing past delinquencies, the creditors do not care what your explanation is. The best thing to do is write to the 3 Credit agencies (Experian, Equifax and Transunion) indicating the account in dispute, with this phrase, "This information is inaccurate, please update the records." That places the burden upon the lender to prove you owe, etc.
Sorry to sound harsh, but I deal with people operating on false beliefs about this every day! It gets a little old.
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C.