Grease 13x9x2-inch glass baking dish. Heat 1 tablespoon oil in heavy large Dutch oven over high heat. Add chard and sauté 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 tablespoon oil in heavy large saucepan over medium heat. Add bell peppers and onion and sauté 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.