Grease 13 X 9 X 2-inch glass baking dish. Heat 1 Tbsp.oil in heavy large Dutch oven over high heat. Add chard and saute until wilted, about 3 minutes. Transfer chard to colander and drain well, pressing on chard with back of spoon to release liquid.  Heat remaining 1 Tbsp. of oil in heavy large saucepan over medium heat. Add bell peppers and onion and saute until tender, about 8 minutes. Mix in chard and toss to combine. Mix in half of each cheese. Season to taste with salt and pepper. Spoon into prepared dish. Overlap tomato slices atop vegetable mixture, covering completely.
Season tomatoes with salt and pepper. Sprinkle remaining cheeses over. Cover with foil. (Can be prepared 2 hours ahead. Let stand at room temperature.) Preheat oven to 350 degrees F. Bake casserole until heated through, about 40 minutes. Uncover; bake until top begins to brown, about 10 minutes more