I'm not to familiar with the new battle.net system. But, I'm assuming if you get one account banned the other will not be IMMEDIATELY banned. But, the other account will probably start to be looked at.
It also probably depends on what you are banned for. If you are banned for something 3rd party related, you may get banned on both accounts because its a program and you may have used it on the other.
If one account gets banned, they can't ban the other account for no reason. So pretty much, as long as you are careful on the account you DON'T want banned, you should be fine! =D