@AnxiousFatherToBe firstly I just want to say you sound like a wonderful husband, who is truly thinking of helping his wife.
For everyone it's so different, so help that is needed will vary, but it's clear you are aware of that.
It's scary becoming a father also, and with the added worry of a wife's Mh it can make this all quite an anxious time for you. Don't forget yourself, and to look after yourself when the new babe arrives.
I will share what I found helpful in my experience, and take what you want from it.
My labour was truly awful and I had a 4th degree tear as a result (very painful) so it changed everything for us when caring for baby in first few weeks. I too have MH isssues that I know my husband was closely watching to make sure I was ok.
So for us...husband always done the last feed before bed and got him to sleep and settled. He was generally better at putting him down that I was. I did all the night feeds during the week and he did Thursday night - Saturday night (we stopped that after a while as I was waking also)
My husband went back to work after one week, so I did all the care during the day. When my husband got home, usually between 2-3 he took over so I could have a sleep/shower.
When I woke, I took over baby so he could go to the gym as that was very much his thing for keeping MH together.
He would then cook my tea and take baby whilst I ate. He would wash up and clean down kitchen after, wash bottles up and sterilize them all, so for the night I had all clean bottles ready to hand.
First thing in morning he would wash bottles that I used over night.
He always gets up at 5.30am and leaves house at 7.30 - if baby woke up in this time, he would take him downstairs so I could deep sleep for an hour or so.
I did all bathing until he felt confident, so when babe was about 10 weeks I guess and then he now baths Friday, Saturday and Sunday.
He would get me to go for a walk with him and baby after work when weather was nice as he knew I needed to have fresh air and change of scene.
When he went back to work, I was still in a bad way physically, so he picked my mum up every morning for me to have company and dropped her hole after.
All these little things really helped me in the early days when we first had our boy, and we were also first time parents.
Now that our boy is 1 the routine has changed again, but we do it to suit us both and have our own 'parts'.
The midwifes and HV will be aware of MH in the past so they will keep an eye, and if she has a good GP like I do, then he regularly checked in on me. I had antenatal depression, diagnosed at 14 weeks pregnant, so they were great at monitoring me. Being as she is a doctor, she will know better than anyone about depressing etc. just make sure she knows she can come to you without judgement, don't be pushy about how is she feeling, but be there.
On day 5 of having my baby I had the blues (look this up to be prepared)
I cried like a baby, proper sobbing and telling my husband I didn't want my baby and I had made mistake and wanted my old life back. He was amazing, he didn't judge me, he knew all about the blues so was prepared. He just held me toght, told me it's okay to feel how I was, that it would get easier and we would do it together. That night, he become my hero. He supported me so much and let me just cry.
I don't really know what else to offer for advice.