Each spouse is liable for repayment of the debts they incur unless the other spouse cosigns or guarantees the debt or the debt is for the acquisition of "necessaries". Typically necessaries are food, clothing, and shelter. I am not sure whether the education acquired with student loan can be characterized as an acquisition of a necessary. It could be. For you to be liable for the debt, the creditor would have to prove that the education purchased was a "necessary."
If you did not cosign or guarantee her loan, then giving her your share of the house in exchange for something that you only might be responsible for repaying (your "half" of her student loan) is probably not a good deal. You need to understand that if she defaults, and the creditor sues you for repayment and successfully proves that the loan was for a necessary, you will be liable for the full balance of her student loan. Whether she "forgave" that debt is not binding on the creditor. The practical question is whether a creditor would be willing to go to the expense of hiring a lawyer and taking you to court to prove whether or not this education was a necessary.
Since creditors are not party to the divorce, any provisions regarding who agreed to pay what are not binding upon them. They will not care and will go by the contract they have with the debtor. Thus, the student loan creditors are much more likely to pursue the makers of those loans for repayment and ignore any agreements or rulings made in the divorce.
If you accepted her offer, you would give up your half of the equity in the house in exchange for a debt for which you may not held liable. However, if you were held liable, it would be for the full amount of the debt and not half.
Much more relevant to your situation than student loans is the mortgage loan on the house. If you are going to give up your share of the equity, and your name is on the mortgage, the loan should be refinanced so that you would not be liable for repayment if she defaulted after the divorce.
The short answer to your question is that you should not be doing this without a lawyer. Any divorce involving substantial debt needs the attention of an attorney sensitive to family law as well as debtor/creditor law.