Idk what to do anymore…am I overreacting

I’m three months postpartum, living in a new country, and having problems with my husband. Honestly, the problems are so up and down, I feel like I can always get over it and be fine. But lately, he’s been so shut off. He rarely talks to me, he doesn’t kiss me, he never asks how I am, and he shows zero affection. He’s great with our daughter, which is amazing. And there are times he’s like this and I chalk it up to being busy and overwhelmed at work (army, new unit). However, he’s been on paternity leave for two months and doesn’t go back till the beginning of July. He is getting deployed next month, and I’m obviously stressed about that. He doesn’t talk about his feelings, and most of the time he acts like he doesn’t really have any. The only time I’ve seen him truly care is when we got into a huge fight about guns (idk i was like 10 weeks pregnant & emotional af) and I regretfully told him that he should just give up his parental rights now since he doesn’t care if our child lives or dies. I was definitely the dick in that conversation.
No matter what I do, or how I bring it up, I get nothing. I try to put myself in his shoes, I try to understand his thought process, I try to give him space. But I feel like I’m working ten times harder than him at our relationship and idk how much longer I can be the only person working on this. Also, for Mother’s Day, he sort of planned a trip out of town. But none of the little things I enjoy, like crafts or pictures or even a card. I wanted a first Mother’s Day card. Meanwhile, I bought him things he loves, plus a card from our daughter and from me. Also we are going on a trip to celebrate Father’s Day and then my bday two days later.
How do I connect with him? What should I do?
TLDR: husband ignores me, what do I do.