Most likely your husband is charged and convicted with Domestic Violence. Anytime someone is convicted with Domestic Violence, s/he is deportable. In your husband's case, there may be a solution if you reopen both battery cases and you testify in court that he did not hit you and present an evidence to your mental condition. These type of cases, post conviction relief, taes about two years to finalize and cost lots of money. The possibility of success depends on teh records of the case, the facts, and the surrounding circumstances.