There are different kinds of disability checks and the answer to this question could vary depending on whether you're talking about social security disability, VA disability, private insurance disability, short term or long term disability from an employer, etc.
State and federal taxes could also factor into the answer as alone his disability might be low enough not to trigger any taxes, but if he were married and your income was high his disability could be added into your income raising the tax bracket.
Bottom line is that he should get his answers through the source of his disability checks- i.e. social security, the VA, his disability insurance company or the human resources department of his former employer. He should also consult his accountant for answers regarding taxes.
Another thing to consider for yourself is that if his disability is related to a long term condition that is likely to get worse over the years you could find yourself financially responsible for his future medical bills.
Again, you both need to learn all you can about the facts and then you can make decisions with your eyes wide open.
The good thing is that it sounds like the two of you are communicating frankly about this issue, which is commendable and wise.