Tear bread into chunks and place evenly into a greased 9x13” casserole dish (this will be approximately 9 cups of bread chunks). Sprinkle half of the shredded cheeses over the bread. Spread vegetables evenly over bread then cover with remaining shredded cheeses and cream cheese. Beat eggs with milk, ground mustard, salt, chives and cayenne pepper. Pour egg mixture over cheeses. Cover with foil and refrigerate overnight.
Preheat oven to 350F. Bake dish, covered with foil, for 35 minutes. Remove foil and bake an additional 15 minutes. Let stand 10 minutes before serving.