My legal residence is Maine (where I work and live). In March of 2011 my husband took a job in Texas. Therefore as of March of 2011, he became a registered voter of Texas, holds his legal residence in Texas, holding a Texas license and his vehicle is registered in Texas. How should we file?

You are resident of Maine and will report all your income. Your husband is part year resident of Maine and will report income earned before shifting to Texas.
Texas does not have state income tax. Your U.S. Tax Return: Working or Living in Two or More states (http://taxipay.blogspot.com/2008/06/working-in-two-or-more-states.html)

For most married couples its best to file your federal return as Married Filing Jointly, but you may want to run the numbers filing separately to see if it helps. In general filing separate may be advantageous if one of you has some pretty high deductions - such as medical. If you file jointly on your federal return you must also file jointly on your Maine rerturn. You should include schedule NR with your 1040ME return - that's where you document the pottion of your joint income earned in state and separate out the income your husband earned while a non-resident. That's how you avoid having Maine tax your husband's TX income even though you file jointly.