One of my favorite ways to teach my kids about their culture is through cooking and through recipes. And in your family, you may have recipes that have been handed down through the generations; share those with your kids, cook with your kids, talk to them about the recipe and the meaning behind it. Every New Years we make black-eyed peas, hoppin' john in my family, and it's a new tradition that I started; it wasn't something that was handed down from my grandmother or anything. But it was something that I wanted my kids to know about, the Southern African-American heritage and the origins of the recipe. But also books, music, art, travel are all amazing ways that you can expose your kids to both sides of their ethnic background.