The NPHC groups are not exclusively one race. Most, but not all, of their members are black. I'll let a member of an NPHC group tackle that one
As for NPC groups, many of the members are white, but by no means all. I can tell you that my chapter did not consider race at all when considering potential members. We have several different races represented, and we're talking about a small chapter! Besides, if a group is going to cut people for the color of their skin, would you really want to be a member?
I'll second RockChalk's suggestion of checking out multicultural sororities. And it can't hurt to go through NPC rush and see what your options are in that department.
Good luck