I'm going to give you two answers; one Federal, one state.
Under Federal law, if your husband does not offer at least 5 paid sick days, he cannot dock an exempt employee for time missed due to illness. However, he also does not have to pay an exempt employee for any work week in which he does no work whatsoever. So in that case, he would have to be paid his full salary for every week in which he worked part of the week.
Let me give you an example. For purposes of this example, I'm going to assume that your work week runs Sunday through Saturday and the employee works Monday through Friday. Let's say he worked Monday, Tuesday, and then went out on medical leave on Wednesday. We'll say he's out for five weeks, then is out for Monday, Tuesday, Wednesday and returns on Thursday. For both the first and last weeks of the medical leave, he must be paid in full, since he worked part of the week.
If your husband offers at least 5 paid sick days, then when those days are used up, he need not pay him at all for the remainder of the medical leave.
Now, let's address NH law, which is slightly more generous. Under NH law, your husband cannot dock him for time missed due to illness for any day in which the employee calls in sick. So he could technically be required to pay him for every single day the employee is out, if the employee is clever enough to call in every single day.
Does that help? Or make it more confusing?