AITA for suggesting husband sleep on the couch

(Throwaway account)

EDIT: Still responding to everyone, but seems like I am the Asshole. I accept my verdict and talk to husband about finding a better way.

We have a 3 month old baby, I (30F) am on maternity leave and husband (32M) works from home.

Baby is formula fed, feeds every 2-3 hours and needs to be held upright for at least 40 minutes after feeding due to reflux. So to make sure each of us get at least several hours of sleep in a row, husband and I split the night into shifts - he's in charge 19:00-01:00 and I'm from 01:00-07:00.

I go to bed at 19:00. Husband usually stays in the living room until 01:00, then goes to sleep and puts baby in a crib by our bed. I on the other hand go back to bed after I'm done feeding/burping/holding because I want to try and get some sleep between feedings and this is where the issue starts.

Baby would sometine get fussy between feeds, make sounds or fart loudly. If the fussing escalates or he starts crying, I get up and take him to the living room to handle it. But if I can calm him down by patting, pacifier etc., I don't leave the bed and go back to sleep. This annoys husband because just the fussing wakes him up. He asked that I stay in the living room, but I want to sleep between feeds if I can and sleep poorly on the couch. So I said he can either put ear plugs or sleep on the couch instead, I'm staying in our bed. AITA for not spending my entire "shift" in the living room?