As others have said, you're better playing as the two classes that share a starter zone.
So Jedi Knight/Jedi Consular or Bounty Hunter/Imperial Agent etc.
Remember that you can ALWAYS go with her in to her class quest areas (the red barrier that keeps other classes out will turn blue as soon as she enters, and you can then follow her) so she'll never have to go and do any bit alone.
The only single thing she'll have to do without you are the odd conversion on her holo-communicator thing.
I'm playing this way with my girlfriend and it's actually very satisfying, especially as you get to watch two storylines progress!
It can be quite a good idea to pair up a healer and a tank (or even just one of those and a DPS.) A smuggler healer and a commando tank, for instance, will probably see you through the Heroic 2+ areas as a duo fairly easily.
I'm playing as a Jedi Shadow tank and my girlfriend is just Jedi Sentinel DPS, and we're finding them quite easy.
The great thing is that you'll rack up the social points just by playing as a duo grouped!