Preheat the oven to 400 degrees . On each of 2 baking sheets, arrange the bread cubes in a single layer and bake, tossing once, until dried and slightly toasted, about 10 minutes; let cool.
Meanwhile, in a large skillet, melt the butter over medium-high heat. Add the apples, onion and celery and cook, stirring frequently, until softened, about 10 minutes. Transfer to a large bowl and stir in the bread, chicken broth, raisins, dried cherries and parsley; season with salt and pepper. Transfer to a 3-quart baking dish and cover with foil. Bake for 20 minutes, remove the foil and bake until golden, about 15 minutes more.