Your DH is supposed to dress nicely. However he is not required to wear a tux or a suit. DH isn't a dress up kind of guy but on formal night for the first cruise he did wear his suit. On the second cruise he actually wore his tux. He looked fabulous!!
That being said, your DH can wear anything he likes as long as it is neat and not a bathing suit. They would prefer that he wears long pants. DH is disabled and sometimes the thought of changing into long pants was too much so he would wear a nice pair of shorts and a button up shirt. He figured that as long as he was sitting that no one was going to see his legs anyway. He has leg/mobility issues so this factored into his decision. But this was never on formal/semi-formal night. He made an extra effort on those nights.
You will get a slew of opinions on this topic. Everyone has one! My opinion is that as long as your DH is neat and clean then he'll be fine. You will see the gamut of outfits from tuxes, military uniforms, suits and even t-shirts. Enjoy your cruise.