Do I have to pay half the house debt if the wife is keeping the house?

Its a tough case, and one you may need to hire an attorney for. Wisconsin, like Arizona or California is a community property state. While you both share the debts, you split the marital property as well. If she is retaining all the value and use of the home, then you may be able to fight it. If you are having it appraised and plan on selling, you may be entitled to half the equity in the home. Either way, speak with an attorney.

This is a tough situation you are in and I would not go at it alone you may need an attorney.
Your best course of action contact a local attorney, either by email or phone, who will protect you and your rights.
The best way to do this is by clicking on the find a lawyer tab on AVVO. Then find one that will offer a free consultation. This benefits you in two way, first and foremost you need to find an attorney who fits well with you and secondly to make sure that they are skilled enough to take on your case. The best case scenario is that you get your questions answered and you get a powerful attorney to help you if you need one.

If your wife wants to have the house awarded to her, she will owe you half the equity. This is determined by the FMV (fair market value) less the current mortgage balance. If you two don't agree on the value of the house, the court will order it to be appraised and usually both parties pay the cost of the appraisal. If there is equity, she would owe you 1/2 the equity and also have to refinance the mortgage to have it put in her name alone. If the opposite is true, that you are upside down on the house where the debt exceeds the fair market value, if she takes the house, she takes it "as is." I don't believe the court would order you to help pay for the mortgage on a house you no longer own. While I am not saying the court couldn't theoretically do that, I think it is rather unlikely.