Baby doesn't sleep through the night

I have a 5 and 1/2 month old baby. Sweetest baby gjrl ever but she doesn't sleep through the night. I bf and give her solids. I know what to do by letting her cry it out but her daddy doesn't want her cry it out. I am a stay at home mom and a student. He thinks i can just stay up with her throughout the night because he works. How can i tell him that we are going down a road that isn't healthy by not letting her cry it out? Please help!! I need sleep. TIA