Spread bread cubes on a baking sheet, and let dry overnight. Alternatively, heat in oven until dry at 250 degrees F (120 degrees C).
Preheat oven to 375 degrees F (190 degrees C). Butter one 2 quart baking dish and set aside.
Melt butter or margarine in a large pan over medium heat. Add celery and onions; cook for about 10 minutes.
Add mushrooms; cook, stirring, for about 8 minutes. Mix in herbs, salt, and pepper. Fold in bread cubes. Add enough broth to moisten. Transfer to prepared dish. Cover with foil, shiny side down.
Bake for 40 minutes. Uncover, and bake for 10 minutes to crisp top.