Feeling extremely burnt out?

My husband and I are both starting to feel extremely burnt out.

Baby is almost 4 months old, nurses when I’m home/takes bottles while I’m away and has CMPI + soy intolerance. I’ve been back to work for a little over a month and my husband is wrapping up his paternity leave while we wait to start daycare full time in January. We have family around, but we are constantly asked questions about baby and if what they’re doing is okay when they offer to watch baby.

My husband openly admits that he is not cut out for baby’s current stage of life and says he has a hard time focusing on baby when there is so much to do around the house. He has a hard time soothing baby, getting baby down for naps before baby becomes overtired and identifying if baby is hungry. However, he has not looked into a single educational resource regarding this, and often resorts to just letting baby scream in his crib or bouncer until baby falls asleep. We have discussed how the bouncer is not a safe sleep space, but my husband continues to let baby sleep there when I’m not available to help out. I’ve caught him swearing around baby on several occasions and have told him he needs to stop as it is not acceptable.

Meanwhile, my husband is still finding time to exercise daily, keep our house spotless, make time for hobbies, watch sports all day on Saturday and Sunday, plan guys weekends away, enjoy a few beers, take an edible to check out and get a full nights rest. I am finding myself somewhat envious. I’m handing all nighttime wake-up’s, baby care when I’m home from work and everything involved in cleaning the house. When I have a free moment, I’m working on chores. I’m fine letting the house get a bit messy, but my husband is not. I also have the significantly calmer demeanor with baby and in general, but I am also just so exhausted and feel like I’m drowning.

Anyways, does anyone have any encouragement or general advice for getting through this stage?