Hello,
So yes that’s common and I too suffered from both issues and yet still at over 7 years out from stage IV treatments the mucus is still a problem.

I was prescribed medication to produce saliva but it didn’t work for me. Also the following was recommended but none of them worked for me; mucinex, biotene, xylitol (xylimelt), nonalcohol mouthwash. Though they failed for me they may work for your husband.

I found that first thing in the morning and several times throughout the day I run hot water, as hot as I can stand. I swish and spit several times. Once my mouth is clear I take small sips and hack it up and out.
Sometimes this takes several rounds but it works!

I then brush my teeth and then brush again with prescription fluoride toothpaste and leave it dry for 1/2 hour ish.

The cough; I was coughing like a fool and then one of my nurses said, let me get you a prescription for Teslon Pearl…what a relief!!!

It took me nearly a year to eat oatmeal so be patient but at least try to keep drinking fluids…I was unable due to choking!

Hope this helps

MOJO