Hi my name is Alison, well when can I start

My husband residence expired in 2008 he was scared to renew it because previously he had got a felony with of drugs. He did a week and 1 day probation, but charges wer dismissed. Ever since then he still worked with his ID and still use his social security we actually did our taxes this year. His ID expired.Now he is 27 and married to me, we. Have a 4 month old son which his the father, baby has his last name and he signed the birth certificate. We are trying our best to see if we can renew his residence but scared he just might get deported. Please help we need opinions! Thank so much