In a bowl whisk together flour, cocoa powder, baking soda, and baking powder.
In another bowl with an electric mixer cream butter, peanut butter, and sugar until light and fluffy. Beat in eggs, 1 at a time, beating well after each addition. Beat in flour mixture and stir in chocolate chips and peanut butter chips.
Drop dough by level tablespoonfuls 2 inches apart onto buttered baking sheets and bake cookies in batches in the middle of oven 20 minutes. Cool cookies on racks. Cookies keep in airtight containers for about 5 days.