You can mix and match, but you're limited to the pieces of that class.
Tactical Escort: Gallant, Defiant, and Vigilant.
Exploration Cruiser: Galaxy and Celestial, Sadly the Envoy is left out.
Deep Space Science: Discovery, Cochrane, and Intrepid
Personally, mine are a Gallant, Galaxy, and Cochrane. keeping with all of their default parts, I'm not a fan of the Defiant or Vigilant, so I just use the default pieces. Same goes for the Cochrane. The Galaxy I kept as a Galaxy because the Saucer Separation animation doesn't use the Celestial details when it rejoins the ship. I know, it's just a small detail, but I find it a bit annoying when i I use it.
It does seem that a lot of people don't know or think you can customize them though. I've seen this question quite a few times in zone chat.