Legal Question in Family Law in Illinois

Not as a general rule. OTOH, there are a lot of relevant facts which you haven't included in your question that might be useful in negotiating a settlement taking into consideration your share of the equity in the house. If you have only one child, your wife would be entitled to C/S in the amount of 20% of your net after-tax income until your daughter is 18 y/o or graduates from high school whichever occurs last. This is the kind of thing you should talk to your lawyer about and he/she should run through several different settlement scenarios with you before you decide how you want to proceed.

A court would probably not approve "giving" her the house in lieu of child support.