Place olive oil and butter into a deep baking dish. Layer in 1/2 garlic, 1/2 onions, 1/2 parsley, 1/2 celery, 1/2 basil and 1/2 tomatoes. Cover with 1/2 potatoes and season with salt and 1/2 cheese.
Arrange mussels and juices on top. Season with pepper. Cover with rice. Repeat with a layer of garlic, onions, celery, parsley, basil, tomatoes, oil and butter. Season with salt and sprinkle with cheese.
Pour enough water into the dish to cover all ingredients. Bake for 35-45 minutes or until all the liquid has been absorbed. If necessary, add some hot water during baking.