There are many ways this could be done:
The obvious and easiest way is the court orders the sale of the house and divide the assets equally. The court may be reluctant to do it when this would uproot the minor children.
One party can buy out the house from the other. The court can order the buyout party to refi and the mortgage will be her sole responsibility. In your case your hu*****and could buy out the house and pay the mortgage alone after divorce. You may have to pay him reasonable rent afterwards.
Another way is to divide the house now, but put the house in some kind of co-ownership like tenancy in common. Both parties will be responsible for the mortgage, upkeeping, and tax of the house. The court would fix a date to divide the assets, normally for several years or when the children are grown up.
The court may also retain jurisdiction to divide the house when the children are grown up. Obviously in such a situation you will also have to pay reasonable rent for living in the house with the children.
Bottom line, is, nobody could tell you what is the best way for you. The house may be under water now, which makes a buyout more attractive. It may be very important to keep the house and maintain stability for your children. Your child support may increase your ability to get a now loan. All these are possible. An experienced family law attorney can help you decide what to do and argue with the court why should the house be sold (or not).
