YANBU. It sounds like lack of sleep and his insensitivity is very unhelpful.
Re "We are both meant to be making a concerted effort to really try and make things work, this just seems petty." It is ....BUT... can you talk together and see if there is a way forward. maybe he wants you close by and to watch whatever, could he have headphones? Maybe he feels pushed out because the twins are taking all of you and he is out of his room.
Re "He hasn't slept in the same bed as me all week. I was really pleased when he came in and thought he was making an effort" please tell him that, tell him you wanted him there, I think he may feel very 'out of it'/away from you.
It's a hard time, a busy time, an exhausting time, but also a lovely time with a new baby, and you've got two! Try and find some fun bits with your dh, make some nice memories, take some lovely photos of your man with your babies.
Money may be scarce but find the joy in little things, I remember when I came out of hospital with dd my husband made me a simple pasta meal (his staple recipe) and it was glorious. He brought me chocolates in hospital and now, almost 12 years later these are memories which stand out for me, along with him helping me to shower because I was quite 'incapacitated' after the birth.
Please do talk to your dh and try and find a nice way forward together. Could you watch those movie trailers together? Can he help with the kids and let you get some shut eye this weekend?
Hope things pick up and congratulation on your lovely twins. 