Jason and Annelia Black, of San Diego County, say the person in the rabbit costume also acted impatiently as their young kids posed for a picture at the Anaheim theme park.
The family asserts things were different when a Caucasian family arrived.
"There were two other kids that came up. The rabbit showered them. Hugged them, kissed them, posed with them, and took pictures. Meanwhile, that made my kids feel horrible," Jason Black said.
The family immediately filed a complaint with Disneyland officials.
They say they were offered VIP passes and $500, but they turned both down.
They were also asked to sign a confidentiality agreement, they say.
The Blacks insist they want a public apology, and the employee involved to be fired.KCBS wasn't able to get a statement from Disneyland.