In a large bowl combine the butter and peanut butter and beat the mixture until it is light and fluffy. Add the brown and white sugars and mix until well combined.
Add the eggs and mix until the mixture is well combined and light in color. Add in the milk and vanilla and mix until blended.
Add the dry ingredients and mix just until combined. Add in the chocolate chips and peanut butter chips. Let the cookie dough sit for 15 minutes before scooping onto the baking sheets. It will firm up as it sits.
When ready to bake, roll into 1 1/4 inch balls of dough and place onto parchment-lined baking sheets leaving about 1 to 2 inches in between the cookies to allow for spreading as they bake. Bake for 8-10 minutes, taking care not to overbake.
Leave the cookies on the baking sheet for 2-3 minutes after baking before removing them to a cooling rack. This will help them set up and be firm enough to transfer without having them overbake in the oven. The cookies may look slightly underbaked but they will firm up as they cool