Combine the milk, water, salt, and cornmeal in a 2 or 3 quart heavy bottomed saucepan. Stir with a whisk to eliminate any lumps. Heat just to a boil (but without scorching). Reduce the heat to very low and simmer the polenta for 25 minutes, stirring occasionally with a wooden spoon. If, near the end of the cooking, the polenta is becoming too thick and heavy to stir, add one or more tablespoons of cold water to loosen the mixture enough to be able to stir it, and to maintain a creamy consistency.
Remove from the heat. Immediately add the butter, the Parmesan cheese, the herbs and stir quickly to incorporate. The polenta can now be served soft, similar to a porridge, to accompany meat or game.