(a) You still file the federal return as MFJ ( Married Filing Joint ) covering you and your husband's world income.
(b) For Michigan, You file joint income ( MFJ )covering you for the whole year and your husband while a Michigan resident ( his world income till leaving Michigan )
(c) Your husband then files a Part-Year Resident return ( MFS ) in Georgia covering his world earnings while a resident of Georgia.
I am assuming here that 1. He is a Georgia resident ---- having lived there for 183 full or part days; 2. He is domiciled / Driver's ,license etc. in Georgia ; 3. He is having Georgia employment taxes being withheld; 4. Michigan does not have a Reciprocity agreement with Georgia; 5. For Household resources computation for MI Homestead credit , Michigan will probably insist that his Georgia income must be included but one could argue ( win or not ) that he is able to contribute ONLY XXX because he is having to maintain a separate household in Georgia.
@Josephine91
Does this help ? Is there more I can do for you ?