I am U.S. citizen and my husband is a non resident. We filed jointly for the last 5 years, my question is can I file head of household and use him as a personal exemption so I can qualify for the EIC credit because he didn't have any income in 2010?

A married person can not be head of household. You can file joint return and get EIC. For EIC it does not matter if one spouse did not have any income. Your U.S. Tax Return: Filing Status: Head of Household