Preheat your oven to 375°F (190°C). Line baking sheets with parchment paper or silicone baking mats.
In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy using a hand mixer or stand mixer.
Add the eggs, one at a time, beating well after each addition. Stir in the vanilla extract until well combined.
In a separate bowl, whisk together the flour, baking soda, and salt until evenly combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix.
Fold in the semisweet chocolate chips and peanut butter chips until evenly distributed throughout the dough.
Using a cookie scoop or tablespoon, drop rounded balls of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake in the preheated oven for 8-10 minutes, or until the edges are lightly golden brown and the centers are set.
Allow the cookies to cool on the baking sheets for 5 minutes, then transfer them to a wire rack to cool completely.
Once cooled, serve and enjoy these delicious chocolate and peanut butter chip cookies with a glass of milk or your favorite beverage!