Cook lasagna noodles to desired doneness as directed on package. Drain.
Meanwhile, heat oven to 350°F. In medium saucepan, blend broth and cornstarch until smooth. Add milk and dill weed. Bring to a boil, stirring constantly. Cook over medium heat for 2 to 3 minutes or until white sauce is bubbly and slightly thickened, stirring constantly.
Spread 1/2 cup white sauce in bottom of ungreased 13x9-inch (3-quart) glass baking dish. Top with 3 cooked noodles. In medium bowl, combine shrimp, spinach and 1 cup of the white sauce; mix well. Spoon half of shrimp mixture over noodles; spread evenly. Sprinkle with 2/3 cup of the Swiss cheese.
In another medium bowl, combine crabmeat and 1 cup of the white sauce; mix well. Spoon crabmeat mixture over cheese; spread evenly. Top with 3 noodles. Top with remaining shrimp mixture, 2/3 cup Swiss cheese, remaining noodles and any remaining white sauce. Cover tightly with foil.
Bake at 350°F. for 50 to 60 minutes or until hot and bubbly. Remove from oven; uncover dish. Sprinkle with remaining 2/3 cup Swiss cheese and Parmesan cheese.
Return to oven; bake an additional 5 to 7 minutes or until cheese is melted. Let stand 10 minutes before serving. Garnish with fresh dill.