My husband and I have worked in the D. R. Congo (DRC) since 2013, and were due to return from a home assignment in Canada June 2018, three months before our baby was due. We had talked with the missionary doctors in and around our location, and they recommended we go to Kampala (Uganda) for the birth, just in case, because facilities in our region are so limited (no NICUs), and because they didn't know if they would have a blood donor for me if I needed one. We had friends who had delivered in Kampala, so we got the name of the hospital and made an appointment with an obstetrician.
We were really pleased with the level of care and the facilities at the hospital. The major differences from home were A) it's private, so we had to pay (our insurance covered it but, as a Canadian, bringing a credit card to a doctor's appointment just feels strange), and you don't really need appointments, but you just find out the doctor's schedule and show up when they are there, first-come-first-served.
Our baby was born by an emergency C-section (which is a story in itself), and I was so happy to deliver in Kampala with our amazing obstetrician. He is a great doctor. He was so patient and encouraging, and so thorough. I really wonder if another doctor would have noticed what was wrong and if they would have reacted quickly enough. He always made sure that my questions were answered, and went out of his way to care for me and make sure I was ready to get back to DRC. We also had a great experience with our daughter's pediatrician, who was there when she was born and then did her follow up appointments.
This is maybe less crucial, but the food at the hospital was so good, the nurses and midwives were so nice, and we had a private room with a bed for my husband, which was all so wonderful (although that might have been the drugs talking...).
I think it was harder on our family than it was on us to have our baby overseas. We were happy to have it be "just us", but I think that was because we already had friends and coworkers in Kampala who helped us and visited us. Having that community was such a blessing, but we were definitely calling our family often, and sending as many photos and videos as we could.
My advice to families in a similar situation would be to do some research. Ask around. We found a great hospital and doctors through our friends, and we had more available to us than we would have had in a small-city hospital back home. But don't assume everything will be the same. Every country (and sometimes every hospital/midwife) does things differently. Know what you need and want, and then ask for it. Our hospital doesn't routinely do StrepB testing, but I asked. They use a different vaccination schedule and get different vaccines than back home, and we chose to go to another hospital to follow the Canadian schedule. Knowing what to expect and how to navigate the system made everything much easier (especially when the unexpected happened).