Arrange eggplant slices in a shallow baking dish; top with a layer of spinach.
Mix tomatoes, onion, and chives together in a bowl; spread evenly over the spinach layer.
Bake in preheated oven for 20 minutes, sprinkle Colby-Monterey Jack cheese evenly over the dish, and continue baking until the cheese melts slightly, about 2 minutes. Cool 5 minutes before serving.