Husband in jail for domestic violence..first time offender..NEED INFORMATION ON IMMIGRATION PLEASE!

You need to consult with an Immigration Attorney as soon as possible, before your husband request Voluntary Departure. You do not provide enough information to give you an answer. For example, what is your husband's current status, EWI, LPR, TPS, etc, and what is your status? Do you have any children born in the U.S.? What is the country to which he will return?

Has he pled guilty or nolo contendre to the Domestic Violence charge? Is it a felony or misdemeanor?

As to your question what will happen if he returns without permission, he will be subject to prosecution under Title 8, Section 1326 as unlawful reentrey of a removed alien with the possibility of a federal jail sentence of 10 years.