My husband doesn't own a tux, too expensive to rent for three nights on a 11 day cruise, so I am wondering would he be able to get into the dining room with a sport jacket and tie?

Yes, no problem. I only bought my first tux about 2 years ago, and before that always wore a lounge suit. I have to say, I did feel a little left out not wearing a tux, but it is perfectly acceptable.
What ship are you sailing on?

We will be sailing on the Brillance of the Seas, March 8th, 2004.....our first, and if what I read hopefully it won't be our last...

Just came back from a week on the Voyager of the Seas and I have to say, save your money! There weren't that many people wearing tuxedos. Men in suits were totally fine.