In a bowl, mix all-purpose flour, sugar, baking powder, baking soda, and salt. With a pastry blender or 2 knives, cut in butter until mixture forms fine crumbs. Stir in whole-wheat flour and oats.
Add yogurt; stir gently. If mixture is too dry to hold together, stir in milk, 1 teaspoon at a time, just until dough holds together; it should not be sticky.
Turn dough onto a lightly floured board and knead gently 5 times to make a ball. Set on a lightly greased baking sheet. Pat into a 7-inch circle. With a floured knife, cut a large X on top of loaf.
Bake in a 375° oven until well browned, about 40 minutes. Cool on a rack. Serve warm or cool.
Nutritional analysis per 1-oz. serving.