Place a large saute pan over medium-high heat and add the beef and sausage. Cook, stirring occasionally, until it begins to brown, about 2 minutes. Add the onions, garlic and dried oregano and cook until they are softened and the meat is cooked through, 3 to 4 minutes. Stir in the tomato paste and toast for 30 seconds, then add the tomatoes and cook until the sauce has thickened slightly, about 5 minutes. Remove from the heat and set aside.
Beat the eggs in a large bowl. Add the ricotta, 1 cup mozzarella, 1/3 cup Parmesan, fresh basil and oregano, salt and pepper and stir to combine.
Spread a thin layer of sauce on the bottom of a 9-by-13-inch baking dish. Arrange a layer of noodles over the sauce and top with a third of the ricotta filling. Spoon over a layer of sauce and top with another layer of noodles. Continue with 2 more layers of ricotta, sauce and noodles, ending with a top layer of noodles. Spoon a thin layer of the remaining sauce over the top, sprinkle the remaining mozzarella and Parmesan over the noodles and cover with aluminum foil.
Bake for 45 minutes, then uncover and cook until the cheese is golden and the lasagna is bubbling, another 15 to 20 minutes. Let stand for 10 to 15 minutes before serving.