Without knowing the full circumstances (as well as your assets and liabilities), it's hard to make a determination of what to do and what to offer. You can ask a judge to give the house to you in a just and right division of property but negotiation is an art and you really have to know all the facts on the table.
The just and right division of a marital estate is a fact sensitive inquiry. You can request the house from the judge in the divorce. You should, however, consult an attorney with regard to whether an award of the house to you would be wise given the totality of your estate.
You mention on-going negotiations and a pre-trial event. Have you and your husband engaged in a mediation with a skilled mediator? Depending on the issues still open in this property division and divorce, you may only need a few hours or a half day mediation. In Dallas, you may also be able to take advantage of Dallas Mediation Services (a low cost service using volunteers), depending on your circumstances. As noted in the other answers, negotiation is an art and reaching a property division is fact intensive. From your question, it sounds like you don't really want the "under water" house, but husband is not putting anything or is not putting what you want on your side of the table. A mediator may be able to get to the why or a show him a way to do that.
This response does not constitute legal advice. The facts and circumstances of any particular situation are unique and require an individual consultation before relying upon the general information contained here. The responding attorney welcomes the opportunity to consult with new clients to determine the appropriate direction and strategy for their case.