Do you work and help with the baby?

Am I wrong to expect my husband to work and help at home with our baby? We just had our baby a little over three and half months ago. I'm ( F25) now on (paid) maternity leave (we don't live in USA). Before that I worked less than PT and I’m in school so I did most of the housework. The reason I am asking is today I was so tired so I asked him (M 34) if I could take a nap and he could watch the baby. He said he is not on vacation (he means maternity leave) like me and I have all week while he is at work to sleep while he is working to provide for us and he should be napping on the weekend. I told him I fully understand but I really don't have energy to function since I woke up many times last night to feed the baby. He rolled his eyes and left the room. Tonight I asked him to cook because I am still so exhausted and he mentioned again that it's unfair that l'm expecting him to help out at home when I'm the one l'm vacation. I lost my temper and said it's not a vacation and caring for the baby is a full time job. He said he’s ordering food and walked away. Our relationship has been rocky since I gave birth. He has been complaining a lot about lack of sex but l'm all alone and tired and healing still (my family live across the country and his family never ever offer help). Am I being unreasonable here?