Heat butter and olive oil in a large saucepan over medium heat. Add onion and celery. Sauté for 5 minutes until soft. Add garlic and cook 1 minute.
Sprinkle in flour and stir to coat. Cook 2 minutes, stirring constantly.
Slowly whisk in seafood stock until smooth. Stir in cream and milk.
Add paprika, cayenne (if using), salt, and pepper. Simmer for 10–15 minutes.
Stir in crab and shrimp. Simmer gently for 5–7 minutes.
Add lemon juice before serving.
Optional: Use an immersion blender before adding seafood for a smooth bisque.
Serve hot, garnished with parsley or chives.