Preheat oven to 325°F (160°C). Spray a 12-cup Bundt pan and set aside.
Whisk together the flour, baking powder, and salt. Set aside.
Using an electric mixer on medium speed, beat the butter, both sugars, and peanut butter at medium speed until fluffy. Add the vanilla, and then add the eggs, one at a time, beating well after each addition.
With the mixer on low speed, gradually add the flour mixture, alternating with the milk, beginning and ending with flour mixture. Stir in the chocolate chips and peanut butter chips. Transfer the batter to the prepared pan and spread evenly.
Bake for 1 hour and 15 minutes to 1 hour and 25 minutes, or until a pick inserted into the center comes out clean. If necessary, cover the top of cake with aluminum foil to prevent excess browning.
Cool the cake in the pan for 15 minutes. Then, remove from the pan to a wire rack to cool completely. Garnish, if desired, with confectioners' sugar.
To store your peanut butter pound cake, wrap it tightly in plastic wrap or foil to keep it fresh, or place it in an airtight container. Keep it at room temperature for up to 3 days.