I transplanted in 2009 for PSC at age of 60.
My experience was a little different - I did not have UC, but did experience acute kidney failure and was on dialysis before transplant. So I was very weak and fragile pre-transplant. Having said that, I received both organs from a deceased donor in one surgery. Immediately upon awakening from my surgery I felt as if someone had flipped a switch inside of me and I could feel a difference. My son called out that I was not yellow anymore. My surgery was on a Wed evening, and on Thursday afteroon I was rolled out if recovery/ICU to my room - sitting in a wheelchair while sipping on a milkshake! On Friday morning, I had a light breakfast and was helped out of bed for my first walk. Each day I felt better, more alert, and stronger than the day before.
During my hospital recovery time, my husband and I were given instructions and guided thru my early recovery process. @svezir, has already shared the importance of caregiver/patient understanding of the importance of follow-up labs as well as medication regime.
I had my transplant at Mayo Rochester, and we stayed at the Gift 0f Life House, where we had been living for the previous 2 months. This was very convenient because after transplant there will be frequent labs and follow up appointments. On Day 21 post transplant we were discharged to return to our home in Kentucky.

Your husband is your and active and healthy. I remember being told by my GI, early in my diagnosis of PSC, that PSC patients do well because they have learned to be proactively healthy and active before/if their PSC progresses to liver failure. It sounds as if his doctors are OK with this schedule, and that is a good sign.

I am going to look at my journal later today, and see if I have any specific recovery notes to share.
Is your husband planning to be active in your delivery and baby's care? What are the transplant doctors saying about that due to his immunosuppression?