I’m at a loss!

My husband and I are trying to figure out some kind of plan on how we can get through these sleepless nights with a newborn. At first we did the “both sleep and wake up when baby sleeps/wakes”. That didn’t work at all. Then, he suggested that I will be up with him all day, and he would be up with him at night so that way I got a good bit of sleep. The first night went well, but the last two nights were hard on my husband despite him drinking coffee like he did the first night. The problem is that we both start to nod off when we try to stay up with him, and it makes us frustrated and scared. I also worry about my husband cause he has to wake up at 3 am to go to work anyway on top of being sleep deprived. I told him we have to find a different method that works better for both of us to get through this, but we honestly have no idea what else there is to try! Any suggestions? What worked pretty good for y’all?

Edit: just to let y’all know, I am breastfeeding and my husband will feed him with a bottle sometimes. Our son is only a week and three days old, he sleeps fine throughout the days, but night time he doesn’t sleep long at all, and seems to only sleep when someone holds him, he doesn’t sleep in his bassinet too well for some reason.