Heat oven to 350° F. Spread the bread cubes on a baking sheet. Bake for 8 minutes; let cool.
In a large bowl, combine the bread cubes, corn bread, and enough broth (at least 2 cups) to make a fairly mushy mixture. Season with the salt and pepper. Melt the butter in a saucepan over medium heat. Add the parsley, celery, onion, and garlic. Cook until softened, about 10 minutes. Add the onion mixture to the bread mixture, along with the apples, nutmeg, and mace (if using); let cool. Add the eggs and gently combine. Spread the dressing in an unbuttered 9-by-13-inch baking dish. Bake until golden brown and warmed through, about 1 hour. If you want a crispy topping, leave uncovered; otherwise cover with foil halfway through cooking. Sprinkle with additional parsley before serving, if desired.