We filed jointly for federal. My husband had unemployment income from mass and did not pay taxes on the income. We owe over two thousand and I don't feel that I should pay it since I did not work in mass and paid all my taxes. Can he file married separate in ma so I will not be responsible for his tax bill

yes, you can file separately in MA. The filing status in MA can differ from the federal filing status.

http://www.mass.gov/?pageID=dorterminal&L=5&L0=Home&L1=Individuals+and+Families&L2=Personal+Income+Tax&L3=Current+Year+Tax+Information&L4=Guide+to+Personal+Income+Tax&sid=Ador&b=terminalcontent&f=dor_help_guides_abate_amend_personal_issues_fili ngstatus&csid=Ador