Your husband may have sleep apnoea.
It's a condition that stops the sufferer breathing for a few seconds, hundreds of times a night. This leads to exhaustion of the sort you describe.
He must go to his GP and describe is symptoms, the GP may refer him for an overnight sleep study which will establish if apnoea is present, and advise treatment.
This should not go un-diagnosed, your husband needs to address this, his long term health could be affected if he continues to ignore it.