My partner is burnt out, I can't show much understanding anymore.

Good morning lovely people,
I just want to vent my heart a bit.
My husband and I have been together for 15 years, soulmates with a beautiful 4-year-old daughter, and for 7 weeks now we’ve had our long-awaited second child, a boy.
It took us 2 years with some help to get pregnant with the second one.
For almost a year now, I’ve noticed that my usually relaxed, easygoing man has become increasingly irritable. He always had endless patience, but he’s become shorter and harsher with our daughter and with me. It only got extreme after our son was born. Not enough sleep, no routine, and bumping into each other led to a very tense atmosphere at home.
Last week, the bomb finally exploded when I confronted him about what was going on. He said he felt numb, empty, and that he currently feels nothing for anything. It was a real blow to me. I had noticed for a while that he was tired, but that he feels nothing for his wife and children is overwhelming. Physically, he’s also shut down—his back and neck hurt him. I was so shocked that I thought about packing my things, but he absolutely doesn’t want that. He says the feeling for us isn’t gone, but he’s full up, nothing gets in.
He went to the doctor but wasn’t helped further. He prefers to be at work, where he has peace and is alone. That really affects me when he says that.
We’ve been going back and forth for about 2 weeks now. We’ve talked more and had a little upswing, but yesterday he came home again feeling down and broken. It affects our daughter when there’s hardly any reaction from Papa, and that affects me too. Now, our daughter got sick last night, and our son is also very restless.
Yesterday, I suggested that it might be better if my husband calls in sick to catch his breath. He keeps pushing himself, but he doesn’t want to.
This morning, he left home. Here at home, it’s chaos with 2 kids who aren’t well, and meanwhile, I’m also running on empty. My mother is trying to help out, but she’s older and not in great shape. Other family members live far away.
I’m finding it hard to show understanding for my husband anymore. He’s so in his own world that there’s little attention for the rest of us.
His burnout is affecting our whole family, and it’s starting to break down...
Sorry if you’ll think I’m mean and heartless for reacting this way to my husband, but there’s so much beauty, and because of his negativity, I’m also feeling down. And this is supposed to be such a beautiful time with my leave.
I don’t know what to do anymore.
I hope you won’t judge me. This is my honest feeling.