My husband has an ugly criminal background, help?!

My family and I are in dire need of a home. My husband and I went to a few apartments and advertised rental homes, we did the routine background checks and my husband's has an unfavorable background. Just when are lives are turning around financially, we now can't get a home because of my hubby's past. Anyway, is there a way he can go to the courthouse and somehow get rid of those domestic violences (note: his ex-wife lied about the DV) and a house theft he committed which occured 14 years ago. My hubby's past isn't up to the criteria of domestic violence at these certain places. My husband's ex-mother-in-law told me he can get it expunged. Is that possible and how would I go abouts it?! Thank you!!!