What company should we dive with in Cozumel?

My boyfriend and I are will be in Cozumel for 1 day on a cruise and were told it is the perfect place for diving. I am a certified diver but he is not. Does anyone know if we can dive together? And also what is the best company to dive with in Cozumel? I heard the Carnival shore excursions were overpriced so I was thinking of booking privately.