Buy Out the Equity
Your house is an asset, so its equity may be divided between you and your spouse when you divorce. If you agree that one of you will keep it, the one keeping it will likely have to buy the other out. For example, if the property is worth $300,000, and if you have a $200,000 mortgage against it, the spouse staying in the home must compensate the other for his $50,000, assuming a 50-50 distribution. If you're the one keeping the home, you can refinance the existing loan for $250,000 and make a cash payment to him, or relinquish other assets worth $50,000 and let him have them instead. If you want to keep the house, keep in mind that you'll probably have to refinance the mortgage anyway, even if you give up other assets to compensate your spouse for his share. You must relieve him of any liability for paying the loan. If your earnings alone aren't sufficient to accomplish this, lenders will generally consider alimony and child support as income under some circumstances.
A Deferred Sale
If you want to keep the home but are unable to swing a refinance at the time of the divorce, you can agree to defer the transaction until a later time when you might be able to manage it. Usually, the spouse staying in the home is responsible for paying the mortgage and other associated expenses during this time, but if you pay down the principal of the mortgage, this will increase the equity with post-divorce earnings. If you stay in the home and pay down the mortgage, you should have something to show for it when you eventually buy out your spouse. You can base the division on the equity that existed at the time of your divorce; for example, your spouse might still receive only $50,000, even if you whittle the mortgage down to $190,000 from $200,000. You would receive $60,000 as reimbursement for the extra equity. Deferred sales are usually hinged to a certain event. For instance, you might agree in your settlement agreement to postpone the sale until a certain date, at which time you will either refinance the existing mortgage or, if that's still impossible, list the property for sale.
An option similar to a deferred transaction is to remain co-owners for a period of time, but this type of arrangement is often more open-ended. For example, you might agree to sell when the housing market bounces back, or when all your children have flown the nest. Depending on the structure of the house, you might even be able to share the residence and lead separate lives, but this is the usually very difficult. In any case, you must negotiate how you'll pay the mortgage and associated costs until you sell the house. If the non-custodial parent moves out, one option is to treat his financial contributions as child support, or he might make the mortgage payments in lieu of alimony.
Split the Proceeds
If you and your spouse don't have an amicable relationship and can't manage a deferred sale or co-ownership, or if neither of you is ever likely to be able to refinance the mortgage into your sole name, you're probably left with no choice but to sell the house. The court will likely order this option if you and your spouse can't agree on what to do with it -- or if you're both determined to have it. You'll still have to make provisions for paying the mortgage until you find a buyer, but ideally, the property will sell relatively quickly. You can divide the proceeds 50-50, or in any other way you or the court determine is fair, and get a fresh start.