Tear bread into small chunks, spread out on a baking dish, and let dry overnight.
Preheat an oven to 375 degrees and butter a 9 x 13 inch baking dish. In a skillet over medium heat, melt the butter. Add the onion, and celery, and sauté, stirring occasionally, until translucent, 2 to 3 minutes; do not brown. Remove with a slotted spoon and reserve. In the same pan, sauté the sausage and beef, stirring and mashing with a fork, until crumbled and cooked through, about 10 minutes. Drain off fat.
Place the bread chunks in a large bowl and while tossing, gradually add the milk. Let stand, stirring occasionally, until the milk is absorbed and the bread is evenly moistened, 6 to 8 minutes. Add the onion and celery, meat mixture, chestnuts and parsley. Season with salt and pepper, add the thyme, if desired, and mix well. Transfer dressing to baking dish and bake, until browned and crispy.