First, you're fortunate that Florida does not have a state individual income tax. So you'll be filing only one state return -- Arkansas.

How you do that, depends on the husband's domicile and whether he has abandoned his domicile in Arkansas.  Domicile has two requirements: physical presence, and intent to stay.  He meets the first, so the question is the second. Does he plan on staying in Florida, and perhaps bringing his wife there when their job situations allows?  Or does he plan on returning to Arkansas when employment allows, and meanwhile gets back to visit as often as possible?  If he doesn't intend to stay in Florida, he's still domiciled in Arkansas -- and a full-year resident for paying taxes there.