There are several different ways to tackle the issue of what happens to the marital home. First and most obvious, the home can be sold with the equity being split in some fashion by the parties.
Secondly, one party can buy-out the interest of the other party. This can be done by acquiring the fair market value from three reputable realtors and taking an average. The party who is going to remain as owner should re-finance the mortgage to remove the non-owner from any liability. Additionally, the party being bought-out should quit claim deed whatever interest he or she has in the property. The quit claim deed should then be properly recorded with the County Recorder.
Thirdly, the parties can agree to remain joint owners of the property until some specific date or time frame (for example, when the youngest child completes high school). Upon the happening of that date or time frame, it can be dictated as to what will happen with the property. It is possible that one party will receive one-half of the equity that was present at the time of dissolution. It is possible that one party will receive one-half of the equity at the time of sale or re-finance.
As you can see, the possibilities are endless and are only limited by the imagination of the parties and their attorneys.
Regardless of what is ultimately decided, make sure that your Judgment and/or Settlement Agreement is highly detailed. There should be no confusion as to who shall pay the mortgage, taxes, insurance and utilities until the property is effectively divided.