Preheat the oven to 350 degrees F (175 degrees C). Line a 12-cup muffin tin with paper liners.

Mix flours, baking powder, baking soda, and salt in a large bowl.

Melt butter in a small saucepan. Stir in peanut butter and brown sugar. Remove from heat and add milk, egg, and vanilla extract. Add butter mixture to the flour mixture, mixing until just blended. Add more milk, 1 tablespoon at a time, if the batter seems dry.

Add apple and peanut butter chips, stirring gently to distribute. Divide the batter evenly among the muffin cups.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 20 minutes.