None. This would fall under accidental damage, which is never covered by AppleCare. In very rare instances is any kind of case damage covered (ie, known defect of product causes case damage, such as the magnet+palmrest problem on earlier MacBooks), but that would not be the situation here if the outer case is damaged.
Even IF they replaced it for you (fee or no fee), they would swap black for black and white for white, since the color you have is the one you paid for.