You can still deduct any mortgage insurance and property taxes that you paid while you co-owned the house. This will depend on when you moved out, whether you continued to make payments, and so on. (For example, if you separated in March, you might be able to claim half the interest from January, February and March.)
Property taxes are a little trickier because they are only deductible when they are paid out of the escrow account. If your taxes were paid in January using escrow money from the previous year when you were helping to make the house payments, then an answer based on equity and fairness might be that you should deduct half.
Also, if house payments were made from a joint account the simplest assumption is that each spouse paid half. However, if you weren't working, or made much more or much less income than your spouse, that assumption might be different.
Ultimately there is no fixed rule. The best situation is to address these items in your divorce paperwork as part of your division of income and property. If the issue is not covered in the divorce order, you and your ex should try and come to some agreement as to how much of the interest and property taxes you will claim as an itemized deduction. If, between the two of you, you claim more than the actual total, the IRS will investigate and decide for you.
Because the 1099 form will be in your husband's name, then if you claim a share of the interest and taxes, you will check the box for "I did not receive a 1099" in Turbotax.
The cash you received as part of the buy-out is not taxable income, because money or property that is transferred as part of a divorce settlement is never taxable. (Transfers that are part of the divorce are different from alimony or maintenance payments that continue after the divorce--those are taxable.)
