You wouldn't have loud music, or hoover, or practise drumming in the room next to someone trying to sleep after a bad night. So having a grumpy, overtired, crying baby in the next room isn't OK either.
You take them downstairs, close all the doors between you and the sleeper and keep them entertained, get them fed and generally try and jolly along. Maybe take them in a walk in the buggy, fetch coffee and fresh bread and hope the cold air makes them fall asleep.
OPs DD may not have been screaming all night, but I remember the long nights of teething well. Baby wakes up crying, you soothe them, administer calpol, try and get them back to sleep, they nod off for 2 minutes and then are back up. You are conscious of not waking your partner up so put them in the spare room with you, where they toss, turn, grizzle, grab, climb, whinge, whine, are uncomfortable and unsettled, they just want to be cuddled on your lap all night. Every time you think they've nodded off and you turn over to get some sleep, they wake up again. It's hideous.
It's like strategic incompetence, so you don't ask him again. Because if you get annoyed and spell it out, then you're accused of nagging or being controlling. It's really selfish and thoughtless of him.