Grease a 3-quart rectangular baking dish; set aside. In a small bowl combine milk and egg. In a shallow dish combine flour, salt, and black pepper.
Dip eggplant slices into egg mixture; coat with flour mixture. In a 12-inch skillet heat oil over medium heat. Add several of the eggplant slices; cook about 4 minutes or until golden brown, turning once. Repeat with remaining eggplant slices, adding more oil if necessary. Drain on paper towels.
Preheat oven to 350 degrees F. In a large skillet cook ground beef, sweet pepper, and onion until meat is brown, using a wooden spoon to break up meat as it cooks; drain off fat. Stir the two cans of tomato sauce and the Italian seasoning into meat mixture.
Layer half of the eggplant slices in the prepared baking dish, cutting slices to fit. Spread with half of the meat mixture; sprinkle with half of the cheese. Repeat layers. Cover dish with foil.
Bake for 20 minutes. Uncover and bake for 10 to 15 minutes more or until heated through. Let stand for 10 minutes before serving.