My husband is loaded with hard masses in his abdomen, chest and groin. He has lost 12 lbs, is exhausted and has chronic cough. But the doctor says nothing is wrong. What could be the problem with him?

Doc is wrong. Either push his doc to do something or go see another doc. Your husband needs a full work up including full blood work (a blood count and complete chemistry panel). He also needs ct scans of chest, abomen, pelvis. A biopsy of one of the masses needs to be done.
He needs an exam. This is worrisome for a variety of problems but it sounds like he needs to see another physician. It may be these symptoms are unrelated and the masses could be clumps of fat (lipoma). This could be a sign of more serious problems like infections or types of cancer like lymphoma. He should see a physician unless your doctor has some explanation for these problems.