What if I paid my security deposit and signed the lease that both me and my husband is on, but my husband has not signed the lease yet? I found a better place and no longer wish to move in the unit again, can I break the lease and get my security deposit back?

If you break your lease, most states require you to pay rent for the lease term or until the landlord finds a new tenant. The landlord will also be required to make a reasonable effort to find a new tenant; they can't just sit around collecting rent from you.