In a large Dutch oven melt butter over medium heat. Cook and stir celery and onion in hot butter about 5 minutes or till tender. Remove from heat.
Stir corn bread, bread cubes, apples, cranberries, sage, thyme, salt, and pepper into onion mixture. Drizzle with enough broth to moisten, tossing lightly to combine.
Spoon stuffing into a 3-quart baking dish (13x9x2-inch). Bake, covered, in a 325 degree F. oven for 35 minutes. Uncover; bake for 15 to 20 minutes more or till heated through and to desired moistness.
