From what you say, I think your husband has eczema. Seborrheic dermatitis is a synonym for this. In retrospect, this never was bacteria, so the antibiotics were beside the point.
Eczema refers to a senstivity of the skin. The face (and eyelids) are common locations in adults. The affected skin develops "dry" patches which are red, scaly, burning, itchy, etc. These spots come and go for no reason. Soaps, moisturizers, or (in women) makeup make the spots redder and itchier but don't cause them.
Eczema comes out of the blue and goes away that way too. In other words, there's probably no way to explain why it's bothering him suddenly.
Topical cortisone creams can make eczema go away very quickly. There are also newer preparations like Protopic or Elidel which can do the same. But--as soon as you stop, the eczema comes back when it wants to. That's just what eczema does--you just reapply whatever cream works.
Don't worry--your husband won't be treating this forever. The condition will "give up" and leaves him alone. Don't know why--it just does.
I recommend another dermatologic opinion. The doctor might suggest allergy testing (to something touching the skin, not a food or drug). Generally, these tests are not useful, but it deserves being thought about.
At the end of the day, though, if the diagnosis of eczema or dermatitis is confirmed, your husband will be able to control his symptoms quite easily and safely with occasional application fo whatever works.
Take care.
Dr. Rockoff