We have not filed for divorce yet, he left me and is waiting until I close on a home to file. The home he is refinancing was only ever in his name, but the money will be going into our joint checking account and then I'll use it as a down payment on a home.
You do not have to pay tax on the money. Payments, transfers, or sales between spouses are never taxable.
Before you make any more major financial moves you should talk over everything with your lawyer. It's not clear from your post whether the buyout has been completed. If not, talk to your lawyer before you go any further.
I am not a lawyer, but it seems to me that you should get your money out of that joint account and into your own account ASAP. If it hasn't actually been deposited yet, maybe it should never go into the joint account in the first place. Talk to your lawyer.
Tax-wise, there's no issue. Divorce-wise, make sure you have appropriate legal assistance. The very first thing my wife and I did when we decided to split was to separate our finances and get individual bank accounts.
The other issue is that if you are not telling the lender that you are divorcing, and you are relying on your combined bank accounts and combined income to qualify for a mortgage, that could be considered bank fraud. Please be careful and get appropriate legal assistance.