I remember watching this sometimes on VHS as a kid when I was going to visit grandparents, so it had to come out before 1990. It wasn’t Bill Cosby himself (the 1983 comedy special) either.
In the one I am thinking of Cosby talked about joining the navy (how his mom was upset and his dad was happy) or how when he was in the navy the drill sargent would knock people out of bed to wake them up.
Any ideas?