Is it possible for one twin to get two of the mothers chromosomes and the other to get two of the fathers?

I was watching Little Fockers last night, and Jack talked about how the son probably got two chromosomes from the father and the girl got two chromosomes from the mother, I know it would be really unlikely in a boy and girl pair of twins, but I have a twin and we're both boys. I don't know, but I'm pretty sure we're fraternal because I look my mothers side of the family and my brother looks like my fathers side of the family. Is it possible I got 2 of my mothers non-sex chromosomes and my brother got 2 of my fathers non-sex chromosomes? Or is that complete movie bull?