I'm not feeling very nervous about meeting her parents, but I just want to know what to expect. Is it like an interrogation? A date?
They probably want to know more about you. They'll almost certainly ask how you met their daughter, what interests you have, what you plan to do once you graduate, etc.. It's super cliche advice, but just be yourself (within reason). Be personable, but not overtly friendly. Laugh at their jokes, but don't go too crazy with your own. Make eye contact often, but don't stare holes through them. There's dinner involved, right? Sit up straight, chew your food thoroughly, use your knife and fork well, stuff like that.
If you're serious about dating this girl, keeping in good (or at least modest) standing with her parents is recommended. First impressions are crucial. It's a fine line to tread and nobody expects you to ace it, but as long as you make a modest effort I'm sure it'll go over fine.
edit: Oh wait, by dinner were you talking about communion? If so, scratch my sentences about dinner.