Is there any rule followed or imposed by commercial airlines that the pilots of a particular plane may not be a married couple? My thinking comes from common workplace rules, where generally HR does not allow a couple to work in the same department, for obvious hierarchical issues.
The Air Force, at least when I was flying there, had strict rules forbidding a husband and wife flying as crewmembers in the same aircraft. Generally, airlines in the US don't have to have any similar policy, and there are plenty of examples of married couples (either pilot-pilot, pilot-flight attendant, or flight attendant-flight attendant) working a flight together.
An individual airline might be able to create such a policy themselves (although I have no idea if there would be legal grounds for a married couple to challenge the rule), but at least in the US there's no legal requirement that prohibits it.