Preheat the oven to 375°F. Line standard muffin pans with 12 to 14 paper liners.
In a large bowl whisk together the flour, baking powder, and salt.
In a medium bowl, whisk together the melted butter, brown sugar, peanut butter, eggs, milk, and vanilla until smooth. Pour wet ingredient mixture into dry ingredient mixture. Stir until just combined. Fold in the chocolate chips and peanut butter chips.
Fill each muffin cup to the top. Bake for 18 to 20 minutes, or until a toothpick comes out clean and the top of the muffin springs back when lightly pressed. Cool in the pan for 5 minutes before removing the muffins to a wire rack to cool completely. Serve warm or at room temperature.