Preheat the oven to 375 degrees F (190 degrees C). Grease a 12 cup muffin tin, or line with paper liners.
In a large bowl, stir together the unbleached and whole wheat flours, sugar, baking soda, baking powder, salt, and nutmeg. In a separate bowl, stir together the yogurt, milk, and vanilla. Add the wet ingredients to the dry, and mix until just blended. Fold in the walnuts. Spoon batter into the prepared muffin cups.
Bake for 18 to 20 minutes in the preheated oven, or until the top springs back when lightly touched. Cool in the muffin pan on a wire rack.