Melt the butter in a medium saucepan over low heat. Stir in the peanut butter until smooth. Add the sugar, then the graham cracker crumbs, and stir well to blend. Press the mixture over the bottom of the prepared baking dish.
Melt the butterscotch chips and chocolate chips in separate bowls in the microwave on high in 30-second increments, stirring each time, until the mixtures are melted and smooth, about 2 1/2 minutes total. Pour the melted chocolate over the crust and spread evenly. Dollop the melted butterscotch evenly over the chocolate and drag a butter knife or skewer through it to make a marbled effect. Refrigerate until the topping has set, 20 minutes. Slice into bars and store at room temperature.