Husband has Maine residence, Wife has NH residence

So my husband and I were married in 2020. My residence and job is in NH, his home and job are still in Maine. We spend the weeks in NH and the weekends in Maine. We filed jointly for our federal taxes,  using the Maine address.  I have a few questions because I think I made a mistake. I have filed the federal but not the state taxes at this point

1) if I filed jointly using  the Maine address as the primary- do we both need to file Maine state taxes?

2) do we have to file jointly for Maine? 

3) would it make more sense to amend the federal taxes and file married but separate?  If I do that, do I still have to file in Maine, or would he have to do it just for himself. Do we keep our own addresses in NH/ME for this process?