Just a suggestion, next time your husband wakes up with his 'heart feeling strange' take his pulse either his carotid (neck) or wrist or even place your hand gentley on the upper left quadrant of his chest. You should be able to feel his heart beat. It should be like this:
lubb.Dubb....Lubb.Dubb....Lub..Dub
record his pulse if you can -- it should be between 60 and 100.
Listen to the consitency of the beat. Does it stop for a couple of seconds? Like miss a beat. Did your doctor do an ecg this shows the rhythem of the heart and will detect any abnormalities at that time.
It does sound like your husband may be experiencing sleep apnoea.
This is when the person will stop breathing for short periods of time in the night whilst they are asleep. It seems to have a predisposition for those who are heavy snorers, overweight, middle aged. I know where im from you can arrange an overnight stay in a specilised unit in our hospital where the client sleeps overnight and is monitored continously by a nurse who take vitals (like o2 stats, heart rate etc) you may want to check it out. I would really suggest possibly seeing another doctor as these types of symptoms can be of a serious nature and should not be present in a healthy fit person.
Hope this helps.