YOU can try to get a mortgage in your name, no problem as long as you qualify. However, the amount you can get approved for depends on only your income, credit, and debts. If you want to use both yours AND your husband's income to qualify for the new home then there will be additional guidelines you need to meet.
Both conforming and FHA lenders have recently instituted "Buy and Bail" policies. Because a ton of people have purchased new homes to take advantage of low prices and simply walked away from the mortgage on their old home, if you claim you are going to rent out your current home then you must some extra guidelines. Most likely you and your husband would have to qualify for BOTH house payments (regardless of whether or not you rent it out), you'll probably need to have 6-12 mos worth of both payments in reserves such as savings or retirement accounts, and any income derived from renting the house cannot be counted towards qualifying on the new one.
Your best bet is to speak with a local, reputable mortgage lender who can walk you through the process to see what you can qualify for. I'm local, and I consider myself pretty reputable, so feel free to drop me a line if you have questions