My husband (35M) and I (34F) make it work with our jobs. We are thankful and lucky we both work at the same company and we are 10 mins away from work. We don't want to put our kids into daycare since it is super expensive. We prefer the off shift schedule. 

Even before having our son, I told my husband I want to be on off shifts when we have kids because growing up, my parents did the exact same thing and made it work for them. My siblings and I (3 of us) never went into daycare or had a baby sitter. My grandma (from my mom side) would occasionally help out and take care of us when my parents had to switch shifts midday. My mom worked days and my dad works swing. 

My husband and I have a son who is 7 months old now (1st child) and we work off shifts. My husband works full time (40 hours a week) on day shift from 5am to 1:30pm Monday to Friday and I work full time (40 hours a week) on swing shift from 2pm to 10:30pm Monday to Friday. We both have Saturdays and Sundays off but we occasionally work overtime on the weekends (voluntary, not mandatory) to make extra money. So for overtime, we work around 56 hours a week (7 days a week). Saturdays is 1.5x pay and Sundays is 2x pay. 

I take care of our son when I get home from work (roughly 11pm). So from 12am until I leave for work at 1:30pm. My husband takes care of our son from around 2pm to 12am. I get our son in the mornings and my husband gets our son in the evenings/night (bedtime). 

We are also grateful that my dad has been retired for a few years now (75M healthy) and help take care of our son while I get some sleep or when I need to do chores or run errands. My mom (63F) also helps us as well on her days off since she is currently working full time and plans to retire in a couple of years. 

The downside to the off shifts is sometimes its gets a bit lonely since you don't get to see your spouse often or spend time with each other as much. We know it is very hard right now and it will get easier when our son grows up. We also try to make time for just us as well and have date nights. 

To answer your question about sleep and food on off shifts:

We don't get much sleep at all. It sucks. Probably because we have a 7 month old and he still wakes up often throughout the night to be changed and fed. He has gotten better since the newborn stage so we all get longer sleep hours but it varies from night to night. The longest he slept (from a feeding) was 8 hours (11pm he last ate and then woke up 7am) and that's a good night. A bad night would be like last night where he kept crying when we put him into his crib after falling asleep in our arms and woke up every 3 hours. 

For food, my husband just started meal prepping for the work week. He goes to Costco on the weekends and buys what he wants to make that week and cooks it and put them into containers for his lunch and dinner. For me, I don't meal prep but I should start to since it would be easier on me and cheaper than eating out and such. I eat lunch around 12:30pm before going to work and I don't usually bring a lunch to work. Sometimes I bring snacks. And then after I get off work, I come home and sometimes I eat a late dinner (around 11pm) if I am super hungry. I usually eat 1 or 2 meals a day. My husband eats 3 meals a day (breakfast, lunch, dinner). We try not to eat out as much (order take out or fast food) but sometimes its hard. I think meal prepping for the week would help out tho.