How to Buy a House with an FHA loan as an unmarried couple?

[Maria Christina Silva]

Is it possible to buy a house as an unmarried couple together with an FHA 3.5% loan if one of the people in the couple has good credit but no steady income (an entrepreneur, not willing to take a full time job at the moment, and not paying himself yet) ... and the other person has steady income, but bad/no credit (credit companies are not accepting applications) ? But we have the 3.5% down payment. Can we combine our names on the purchase if we're not married, and will they accept those circumstances from both of us together?

If so, why? If not, why? And how can we possibly get passed this?