I'm half Korean, half German (lol, definitely not an advantageous combination).
I had that very same dilemma, but I just decided that I'm going to put both.
I know what they say about Asians and Whites concerning college admissions, but I figure there's no way around it.
I can't change my ethnicity and even if I don't fill in an ethnicity, they'll assume I'm either White or Asian just by my last name (it could actually go both ways, oddly enough).
And besides, they probably know that if you leave it blank, you must be Asian or White anyway because a URM would most definitely take advantage of the situation.
I know I would.
But let's just hope that it's our skills that get us into colleges, not our debatably disadvantageous ethnicities.