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 saute, stirring occasionally, until translucent, 2 to 3 minutes; do not brown. Remove with a slotted spoon and reserve. In the same pan, saute 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 a baking dish and bake, until browned and crispy.