How to co parent in the same house???

So my son is a month and me and fiance are trying to do it together.... I'm breastfeeding and wondering how he can help with that I pump milk so he can feed him when I'm doing grocery shopping or something when I'm outside because I'm off of work until Feb and he goes back this week but he says he wants to bond with our son by feeding him and I ask him to burp him and change his diaper after I finish feeding him because I be so tired and I told him not to use the milk in the fridge because if I'm home I can feed him but he says that's not enough bonding I guess this is my 1st baby and his 5th and he claims he know what to do but in the 6 weeks he's been off he has fed him cuz i was on antibiotics for 10 days because I had to pump and dump I had to give him formula because we ran out of breastmilk and I dont want him to use formula but his father doesn't care but I do I'm trying to pump and breastfeed but I really don't know how can someone help???? I love my fiance but we've been having a lot of disagreements lately and when our son wakes up in middle of the night sometimes I sleep thru him crying and I feel bad and sometimes he sleeps thru it too mostly but at different times though and I tell him to wake me up and when I finish feeding him and try to burp him I fall asleep with him on my chest and he gets upset but sometimes if I put him down right after he wakes up and he doesn't really like the pacifier so I put him back on the breast until he falls asleep and then we fall asleep together or if I have to use the bathroom and he's hungry I feed him while I'm using the bathroom because I don't like to hear him cry but his dad don't like it when I'm on the toilet feeding our son he rather me wake him up so he can watch him but he would scream and it's so much easier for me to just give him the breast instead of him warming up a bottle to feed him and he's old school and heats up his bottle in the pot and I told him I would get the bottle warmer but he say we don't need it but he turns on the light and gas and I've been trying to save so we can move into a bigger apartment when he goes back to work idk how he's going to bond with our son since he works from 6am to 5pm mon thru Friday????

Our baby boy Zyon