Preheat the oven to 375 degrees F (190 degrees C).
Lightly grease a baking sheet.
Mix all-purpose flour, sugar, baking powder, baking soda, and salt in a bowl.
Cut butter into flour mixture with a pastry blender or 2 knives until the mixture forms fine crumbs.
Stir whole-wheat flour and quick-cooking oatmeal into the butter mixture.
Gently stir yogurt into the oatmeal mixture. If mixture is too dry to hold together, add 1 teaspoon milk at a time, just until dough holds together; it should not be sticky.
Turn the dough out onto a lightly floured work surface; knead gently about 5 times to form a ball.
Place the dough in the center of the prepared baking sheet; cut a large 'X' in the top of the loaf.
Bake in preheated oven until well browned, about 40 minutes; transfer to a rack to cool. Bread can be served warm or cold.
