Miljet is correct - the shower should drain to the grey tank. However, I have heard more than several stories of people having their black and grey tanks labeled backwards (either on the tank level indicators, on the discharge levers, or both). My in-laws even found that the shower in their new 5-er incorrectly drained to their black tank. They took it back to the dealer to have it fixed, but it was still pretty inconvenient.
Unless you are sure where the shower, sinks, etc. drain it may be worth some time to experiment with it. The next time you are at a dump station or at a site with full hookups you might try just running a bunch of water through the shower to see which tank fills.