Preheat the oven to 350 degrees F (175 degrees C). Line an 8-inch square baking pan with parchment paper.
Place unsweetened chocolate, butter, and semisweet chocolate in the top of a double boiler over simmering water. Stir frequently, scraping down the sides with a rubber spatula to avoid scorching, until chocolate is melted, about 5 minutes. Remove from the heat and cool to room temperature, about 10 minutes.
Whisk sugar, eggs, and vanilla extract together in a large bowl. Whisk in cooled chocolate mixture. Stir in flour with a spoon until incorporated. Stir in dark chocolate chips and peanut butter chips.
Spread 1/2 of the batter in the prepared baking pan. Take 1/2 of the peanut butter and put it in small dots over top of the batter, then use a knife to spread it into a marble-like pattern. Top with remaining batter, dot with remaining peanut butter, and swirl again.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 25 to 35 minutes. Let cool completely before slicing.