Layer 1/2 of the tortilla chips in an even layer on a baking sheet. Top with 1 cup Swiss cheese, 1/2 cup Cheddar cheese, and 1/4 teaspoon dill. Repeat layers on top.
Bake in the preheated oven until cheeses are melted, about 5 minutes. Remove from oven. Set an oven rack about 6 inches from the heat source and preheat the oven's broiler.