The ability of different liquids to mix completely into one another is called miscibility. While water-soluble compounds dissolve easily in water and fat-soluble compounds dissolve easily in oils, the two can mix with the help of molecules called emulsifiers.
These molecules are large enough that they can be polar on one end and nonpolar on the other end. One well-known natural emulsifier is egg whites. The large protein molecules that make up the egg white have parts that bind with polar molecules and other parts that bind with nonpolar molecules. This is how adding eggs to cake mix allows oil and water to mix together evenly along with the other ingredients. Fortunately for the nutraceutical beverage industry, more sophisticated methods than egg whites have been developed to help make nonpolar substances miscible with water.