Is it rude?

My husband has a terrible cough and everytime he coughs he wakes up our baby. Our baby is pretty easy so he eats and goes back to sleep, but it's still annoying and no one gets any sleep really because of this. I really feel for him, it sucks to cough, but oh my god it's frustrating. We have an extra bedroom but anytime I tell him to sleep in another room he gets really upset and starts to argue. Is it rude to ask your partner to sleep in another room so you and your baby can get more sleep?