Combine the milk, water, and cornmeal in a medium sized saute pan. Cook over low heat stirring constantly with a whisk until the mixture thickens (approximately 1/2 hour). After removing from the heat stir in 1-teaspoon butter and 1 teaspoon olive oil.
In a saute pan, cook the mushrooms over high heat with 2 tablespoons olive oil and 1 tablespoon butter for 3 minutes. Season to taste with salt and pepper.
Heat 1-tablespoon olive oil in a saute pan. Lightly flour the cod with the instant flour. Place the fish in the pan and add 1-tablespoon butter. Cook for 3 minutes and then turn over. Place the pan in a 400-degree F oven for 2 minutes to finish cooking the fish. Salt and pepper, to taste.
Place a small mound of the polenta in the center of the plate. Place the cod directly on top of the polenta. Spread some of the mushrooms around the fish and drizzle the olive oil and balsamic vinegar around the edge of the plate.