Most lenders will assist you in choosing the best way for you to apply for a mortgage.
That being said, I suggest verifying your husbands credit history at http://annualcreditreport.com This site is free once every 12 months and you can have access to all three credit reporting agencies to see if there are any discrepancies. The site allows you to dispute discrepancies online.
HUD, also offers housing counselors, who for a fee will assist you and your husband to decrease your debt so you both credit scores can be raised. See the right hand column of this website for counselors and home buying programs (you may qualify)
There are many lender members available on Trulia that might be good choices. There is also a list of companies on the HUD website, or you can try http://mumloans.com They were offering free pre-approval.
You may want to consider someone you know who can be on the loan with you as a "non-occupant co-borrower" to help you qualify. The person doesn't have to live with you but can use their income and credit to help you qualify. In most cases, lenders would prefer someone who is related to you.
P.S. FHA (or lenders doing FHA) generously accept FICO scores as low as 580 (sometimes lower), depending on the lender, so you may still be able to include your husband's info. FHA loans are "story" loans, meaning that if you have a good explanation of your husband's job history, you may still be able to use his information.
I hope this helps and good luck with your home buying venture! I hope you find what you're looking for in a home!