How do I discuss hearing aid adjustments with my Husband who constantly mumbles?

My husband wears an hearing aid. Deaf in one ear. Your husband may have lost more of his hearing and if so needs to go back to the audiologist and have the aide adjusted. The range up and down may need to be reset. Also, wax can get into the tube, if he has an over the ear, and makes it hard to hear. Digital aids always need some kind of adjusting. My DH goes once a year to get it cleaned and tubing replaced because it gets brittle. If he hasn't been for a while maybe he needs to go.

It sounds as if there are other issues other than a single hearing problem.

Several different things may be involved here. I doubt if the problem is with the hearing aids because what you are pointing out is with his responses. I don't know what other medical issues he may have that are involved but a good detailed discussion with his doctor would be a start. For example, Parkinson's patients, like myself, think we are speaking loudly enough, but are not. We sound the same to ourselves but the tendency is for the voice to soften. What sounds to us as though we are shouting actually is just a
normal level of volume. Here's where a referral to a Speech Language Pathologist and some therapy would be useful. Also consider that he may have something going on in his brain so although he "hears" clearly, it now takes him longer to process and understand what was said and to respond. That can easily happen if someone is having some type of mental decline. And maybe then his response is a bit confused which inadvertently covers up by mumbling. I think the best plan would be to have him be seen by a SLP for an assessment and for speech therapy sessions. The SLP can also do some cognitive testing. Maintaining speech is important for social interaction and is an issue that can be treated. If you want to try something at home on your own, download an app on your phone that measures sound decibels. I have Sound Meter HQ PRO on my phone after I had speech therapy so I can check on myself if needed. You can measure various sounds around you. You could try recording his speech, and if it is lower than normal speech levels, point this out to him and the doctor to get them convinced of the need for an assessment and therapy. Good Luck in getting some action here. There is an opportunity to improve this situation.

Ask for a referral to a speech therapist.

But first get him to the doctor for a physical and see if anything else is amiss.