Can I sell my current home and purchase a new one while separated?

We are separated (not legally) and I can no longer afford to live in our home and be the only one paying anything on it. We live in a subdivision out in the country and I cannot afford the gas going to and from work and I can no longer afford the dues and assessments charge on only one income. What if my husband were willing to sign a notarized contract relinquishing all claims on the current home and it's equity and then sign another notarized contract relinquishing all rights to claim the new house.