I totally understand! I have twins, and I did most of the care for the first few months of their life, including almost all of the night feedings.
In my experience, it didn't do me a whole lot of good until my kids were older and he was able to really interact with them more. But hopefully it is different for you.
Maybe try explaining to him that while, yes he does bring home the money and works many hours to do that, at the end of the day he gets a break from all that, including days off. But as a parent, you don't get time off or days off...and you would love him to be a bit more involved so you can have time away from your job too. I have always considered a family (even one with just one breadwinner) is a team effort between both parents. After all, you take care of the kids so he doesn't need to stay home with them. You both have duties to do, and both deserve time off from them.
Hopefully you get it worked out, and just know that if it doesn't turn out the way you are hoping, it does get easier when they get older. My kiddos are 20 mo. old, and though they still wake up once a night or so (more if they are sick or the neighbors are making alot of noise) it is usually a simple fix and a quick soothe that they need and then its easier to relax.
If the second scenario is more likely, here is something that worked great for us. We started a bedtime routine (just assuming that you might not have already started this) with our kiddos when they were about 2 mo. old..amazingly enough, Dad did help with that lol. We bathed them, rubbed them down with night-time lavendar lotion (johnsons smells amazing, and is so mild) fed them a bottle (or sippy when they got older) and put them to bed on their own with a comfort toy, a thin blanket, some sort of background noise, and a nightlight. They get used to falling asleep on their own so it gets easier. We also put them to bed around 7 pm so they have the chance to get a good amount of sleep (though they don't nap as long during the day) and so we can un-wind and have time to ourselves before we too go to sleep. Though they do tend to get up a bit earlier. Our kids sleep about 12 hours a night...maybe you will be lucky with that too lol.
Anyways, good luck!! I really hope it works out well for you, because I definitely know that frustration!!