He also revealed that the nanny works 8am-3pm weekdays and as soon as he gets home he takes over dad duty until bedtime.
The post, that has over 780 comments has caused a heavy debate with Redditors.
"Getting up at night is an inevitable part of parenting. You signed up for this when you had kiddos, one person wrote.
Another agreed: "Childbirth is hardcore. Delivering twins via C-section? That's major trauma. She's still recovering from an extraordinary physical ordeal, and she may be struggling with PPD. It's only been three weeks! Let the woman recover."
However, some said the father's request was reasonable.
"70+ hour work weeks isn't doing his part?", one commenter asked.
"I get that the internet tends to be significantly more sympathetic to women, but this is ridiculous."
Another added: "I'm sorry, but the [mother] gets a nanny to take care of the kids during the day and help with house chores, he helps with the kids as soon as he gets home... given the circumstances, I'd say it's fair to have her to most of the night wakeups."
After the thread exploded, the father was not happy about aggressive comments.
"Apparently I'm getting flamed. I don't need to be called a piece of s***. I came here for a legit AITA and for thoughts. Insulting me isn't constructive in any way," he wrote.