The Too Human demo allows access to the other four classes found in the full game, besides the Champion.
To unlock them you need to use a simple workaround found by clever-clogs G4.
Disconnect from the internet and, in the Xbox 360 dashboard, change your console date to any time in or after 2009.
Then, start a fresh campaign in the Too Human demo, and the Berserker and Commando should already be unlocked in the character selection screen.
To access the Defender and Bioengineer, flick the left analogue stick to the right as you select either class by pressing A. When your campaign begins, you will be whichever of the classes you selected.
Too Human is due out exclusively for Xbox 360 on 29th August.