Is it normal or unusual for me to care for my 2 month old baby day and night while my husband will play with him for like 20 minutes tops when he comes home from work?

He does pay for a nanny once a week to contribute and runs a business. Btw, our son has been turning away from my husband the last couple of days when he picks him up. It was kind of funny but I don’t know if they are even aware of stuff at this age