That's pretty much what it is on Princess. Theoretically a coat and tie should be worn on semi formal nights too, but that isn't enforced. There will be two formal nights onboard. They have alternative dining on Princess and if your husband doesn't want to dress, maybe those would be the nights to try the alternatives. I think Sabatini's would probably be dressy but The Painted Desert shouldn't be.
You go girl! Sometimes the guys just need the ultimatum. On our last cruise there were 2 formal nights, and I told my guy that he had to dress up for at least one night. When we got on the ship, we had a table for four, and we got on fabulously with the couple we just met who were seated at our table. They begged him to come to the second formal night. When the next formal night rolled around, I told him that I was going to the dining room to have dinner with them, and he could eat at the buffet if he wanted to. I told him I didn't pay all this money to eat fried chicken and ham from the buffet!
On Princess, "Formal" does mean Formal (tuxedo or dark suit for gentlemen) and "Semiformal" does mean Semiformal (coat and tie for gentlemen) -- and there is an expectation of corresponding attire. Enforcement was lax for a while, but I have seen several indications of stricter enforcement on my last couple cruises. If it's any consolation to hubby, tell him that formal nights usually have even fancier fare than the normal menus served on casual nights.
According to the current edition of Princess's Cruise Answerbook, a seven-day cruise "typically" has two formal nights, one semiformal night, and four casual nights. Several posts on this board have indicted that MV Grand Princess dropped the semiformal night in favor of an additional casual night -- but so far there have been no indications that any other Princess ships have adopted the same policy. On my cruise (twelve nights) aboard MV Royal Princess last month, we had three formal nights, three semiformal nights, and two casual nights, so it seems pretty clear that dropping semiformal nights is not a fleet-wide Princess policy. I recommend being prepared for two semiformal nights (an extra dress shirt and tie don't take that much space, and a cocktail dress is acceptable for ladies on casual nights), as I have been on several cruises where there was an opportunity to participate in a special event that required semiformal attire as well as several cruises where there were more semiformal nights than the number indicated as "typical" in Princess's Cruise Answerbook.
If your husband really despises dressing up for formal nights, though, you might want to check into Norwegian Cruise Lines (NCL) again for future cruises. NCL has adopted a "formal optional" policy -- meaning that casual attire is always acceptable. Such a policy might be more accommodating to your circumstances.