What kind of work does he do nights? I worked nights just 5 days/week and could not get enough good sleep during the daytime to carry me thru the week. I was single and slept nearly the whole day and night my first night off. I was a police officer on patrol.
So both of you are really tired. Try taking a more positive approach. Sit down with him at a time when you're both reasonably rested and won't be interrupted and empathize with him. Tell him that you do understand how tired he is. Explain how tired you are too. Suggest that the two of you find a way to organize life so that both of you share and neither one of you feels like they're doing all the work. If he hasn't taken care of the children for any length of time you'll probably need to describe what your days and nights are like.
Do not criticize him in any way. Tell him you realize he's really tired but so are you and you do need his help. Once he agrees to provide some help then talk about chores and which ones he's like to do. I suggest that you make a list of everything that has to be done every day, every week, every month. Then both of you spend some time thinking about the lists and ways to divy them up.
This will probably take 2-3 sessions to build the basics and the several weeks to work the kinks out. Keep in mind that both of you need to give each other lots of praise, accept the way the other person does their chores, and never criticize or blame. It's a bit like motivating children. Everyone thrives on praise. Everyone gets frustrated, irritated, and even angry when they feel criticized. These negative feelings then prevent us from working well together.
Keep reminding yourself that he and you are on the same side even tho he's not had the experience or training, or even the expectation that he help at home. This generation is coming out close to a generation in which wives worked in the home and husbands outside the home. We;re still dealing with that perception. It takes time to make changes.
While you're working this out, schedule in time for just the two of you to do something fun together. Brush off your senses of humor and try to find the funny side when things go wrong.
And, each of you, also need some time for yourself.
All of this takes planning. When we just live from day to day without thought of how to make the days better we do get in a rut that is difficult to get out of.
Remember to ask him to help in a friendly tone of voice. When you need something specific done tell him what it is. If he doesn't do it, tell him how that hurt you. Leave out the sarcastic and angry words. Focus always on the fact that both of you are doing the best that you can do and that both of you can make changes together when you're working together instead of trying to force someone or just expecting someone to do something.