Is it mathematically possible to be 1/3 Italian?

Is it mathematically possible to be 1/3 of an ethnicity? I won't go into how this debate came up between me and my brother-law, and neither of us are smart enough with math to disprove the other on paper, so I'm hoping someone here can provide an answer.

He says it is NOT possible to be 1/3 mixed ethnicity because, no matter what, our makeup is always a product of two. There can only ever be two contributers, and thus no matter how many hypothetical generations we go up a family tree, and how we slice and dice the possibilities, a person can never become 1/3 of anything.

I say, since the hypothetical ancestral possibilities are infinite, that no number can be excluded from a possible result, and that there simply has to be some combination, even if it take 100 generations of division, that will result in a person being exactly 1/3 Italian (or substitute your favorite ethnicity).

Who is right, and can it be proven?