Hmm, tricky actually, as you say he has had MH issues. From experience, I know that this can make people very tired (and frequently people also "use" sleep as a means of escaping from the world).
I'm going to suggest a different tack to the others.
Sit down and say to him: I recognise that you are tired. I understand that you are tired and need to rest.
Then say: I am tired too, because the 1st trimester is tough.
Instead of making it a competition, or putting him, or yourself, in the position where you have to "compete" for sympathy or the right to sleep, why don't you both acknowledge that you are knackered and try to find ways round that. Don't fight it, IYSWIM. If he can't look after your LOs because he is tired, and thus resents you napping, which I agree is aggravating and unfair, perhaps you need to look into getting a babysitter for key points during the week.
My DH is always tired. He was like this before DD, and was so throughout my pregnancy and now that she's nearly 1yo.
I've had to accept that he has much, much lower energy and resources than other people, and, crucially, me.
Sometimes it drives me up the wall; but he can't help it. He really is crushingly tired (he also has MH issues, and, I suspect, undiagnosed chronic fatigue syndrome). It's so annoying when I am also shattered, and want a break; but sadly he is not the person who is going to be able to give me that break. It's not a question of him supporting me or not supporting me. He's just physically incapable of it. I just have to adopt other strategies for coping. If your DH is anything like mine, I'm afraid you have to as well.
I really hope you get the rest you need and deserve, somehow.