I'm not a health profressional, but I've had bypass surgery and this is not an expected outcome. I'd insist that your husband have a sleep study to determine what is happening. What tests have been done? Please, keep us informed.
I have seen similar issues like this caused from small "air embolisms" that are left/created in the blood stream after the surgery. The doctors take great care in trying to minimize the potential for these air bubbles to be in play but some of them will form as a result of the cooling of the blood before/during surgery to warming it back up after the surgery is finished. The process helps lower the risk of possible brain damage and clotting issues. The problem is simple physics, when the blood is warmed back up the molecules of water in the blood will start "offing" small amounts of air. Think of an extreme case where you boil water, all of the air bubbles are the result of the "offing" of the air molecule. The air bubble/s can then travel anywhere in the body even the brain. If the air bubble sticks to the area of the breathing control center in the brain stem, you can see this type of breathing problem occur. There is a little more to it but for simplicities sake we will leave it alone.
To fix this there are a few tricks up their sleeves, the one I really like is the fluorocarbon slurry flush. It was developed by doctors working with deep sea divers that suffered from the "bends" (air embolisms in the brain). They use an IV to put the fluorocarbon slurry into the blood stream, and it acts to create a"silicone pathway" for the air bubbles to slide right through and break up into smaller bubbles at the same time, that can pass to a point where they are no longer a danger. This is a relatively new procedure, some surgeons will make this treatment part of the surgery for best outcomes. Some are using it post-op as needed, others have never used it (or even studied up on it), so there is no telling what type of response you might get if you bring this up. If they are not aware, there are medical websites they can "Google" to get up to speed.
To be clear, I am not saying that this is the problem, 100% sure. But it fits his symptoms and matches other cases of similar complaint/makeup.
Best of luck