Well… yes
and no…
For a Catholic and a non-Catholic Christian? Right. It’s
possible (although not a given) that permission might be received for a wedding in the non-Catholic’s church, under certain particular circumstances. Even then, though, there’s an expectation that the wedding will be in a church and not, for example, on the beach.
Again, this depends on the circumstance: for two Catholics, it would be odd
not to have a Mass. For a Catholic and a non-Catholic Christian (like the OP’s situation), it would be possible to have a Mass (although, as tee_eff_em points out, not necessary). For a Catholic and an unbaptized person, a Mass would be inappropriate, and a simple wedding service would be recommended.
Well…
In certain circumstances, it’s possible to get a dispensation from form, such that a non-Catholic minister might preside over the wedding. Of course, this wouldn’t be proper if both are Catholic (although this isn’t the OP’s case, I just want to make sure that there aren’t any misunderstandings here). And, of course, if the wedding between a Catholic and a non-Catholic Christian were performed in a Catholic church, there wouldn’t be the possibility to grant permission for a non-Catholic minister in
that situation, either.
Have I muddled the situation thoroughly enough, yet?
It comes down to this: the requirements (and possible permissions/dispensations) vary greatly, depending on the couple themselves and their religious affiliations. It’s best to just ask your priest, and go with what he says…