Yes you can use both bat the same time. Think google just wants users to know the difference between theirs and adbrite. So as google has their branding on their ads so must adbrite.
You should always double check something this important with the Adsense TOS and not take the advice of people in forums - not even me. Full disclaimer: I don't use Adsense and don't pretend to know the current TOS in detail, but the last I knew the restrictions were against 'contextual ads' or ad banks that looked like and could be confused with Adsense. So look for something about that in the TOS then you need to find out what ad formats Adbrite offers and see if there is a conflict.
you are welcome to use any number of adsence with many campaign running for several keywords , that's not a problem for google , only for us who spend money