My husband is prone to be much the same and needs a lot of help/support from me. Life is a lot for hardworking husbands/fathers. We have great ability to help them immensely by taking care of their bodily and emotional (for lack of a better term) needs. To be their light and encouragement, their soft place to land.
It would be hard to say without more information, but to me I would start with nutritional deficiencies. Deficiencies can cause a lot of bodily stress that show up as insomnia, inability to regulate stress, irritability, etc.
How is his diet? Is he taking any sort of supplements? If you can get past the exhaustion, things could really look up.
If your husband is anything like mine he is not going to bother with researching what kind of supplements to be taking or make dietary changes to live more healthfully, but if I do all the legwork for him he will happily do it. It’s not that he doesn’t care, he’s just very busy and doesn’t feel like he has the time to devote to it. I give him different supplements that have helped his nervous system and we’ve also carved out time in the family schedule for taking daily walks. I make sure he gets plenty of healthful food and don’t bring unhealthy processed food in the house. These 3 things alone have helped his mood greatly.
Also, on his days off I prioritize him sleeping in. I get up at the normal time and shut our bedroom door so he doesn’t hear the hustle and bustle of the rest of the family. I make sure to let him know that I am happy that he gets the opportunity to sleep in so he doesn’t feel guilty or obligated to get up. Then we he does get up, be happy to see him and let him decide what is on the to-do list for the day instead of laying the pressure on him.
My husband is out the door by 5:30 am on weekdays so I get up very early to make him a smoothie with ample amounts of protein, collagen, fruits and veggies, etc. I mix up his electrolytes for the day and set all his supplements out and pack him a nutritious lunch.
For him, a lot of stress release comes from being taken care of and prioritized. If I manage to stay cheerful and encouraging despite his grumpiness, the whole house is much happier. I usually try to meet him at the door when he comes home from work and eagerly listen to his challenges of the day, encourage him, etc. I gauge his mood and let that determine whether it’s a good time to talk about pressing matters. I make sure to not start in on my own troubles right when he walks through the door. If I can see that he’s in a tense mood or has had a bad day, I take extra care to keep the kids contained.
Do your best to make the home inviting and a place he looks forward to coming home to.