No matter what, people are going to be discriminatory. I am a (single) mother of a 7 year old biracial girl. Her father is black and I am white. In our small community, there are a growing amount of biracial children. I worried when she was younger about how she would deal with things and she really has surprised me.
When I went to pick up her and a friend (who is also biracial) at daycare last year, a little girl ran up and asked her where she was going. My daughter told her that she and her friend were going to go play at her house. The little girl told her "well I know why she is going with you. Because you are both have curly hair and you are black!" Her friend was stunned, but without missing a beat my daughter told her "No, my dad is black. My mom is white and I'm BROWN." And grabbed her friend's hand and off they went.
I have to say after all the discussions and awkward encounters with people, I was very impressed. Still we encounter times when people, mainly smaller children say "Is she your daughter/is that your mom? You don't look anything alike." and sometimes she will look to me to see what my response will be, but others she will respond with "well I just look a lot like my dad".
Your children see how you react to situations and they learn from it. I have not always handled things perfectly, but I hope that if I can help to ensure confidence in my daughter in WHO she is...as a WHOLE, I may not have been that terrible.