Polymer-stabilized double emulsions are produced by a two-step process, high shear emulsification in the primary and membrane emulsification in the secondary. By repeated fractionation after each emulsification, we obtain monodisperse double emulsions with the size of the complex droplets ranging from submicrometer to a few micrometers. With osmotic pressure balance between the inner and outer phases, the polymer-stabilized double emulsions remain stable for a year at room temperature without structure deterioration. We generalize laser light scattering to probe the structure and internal dynamics of the complex system by including the effects of the amplitude fluctuations of the scattered fields. Both static light scattering (SLS) and dynamics light scattering (DLS) can resolve the inclusions inside the complex droplets. Water-soluble nonionic surfactants are used to induce destabilization of double emulsions. We find that a double emulsion turns into a simple emulsion within a minute at a surfactant concentration of less than 10(-3) mol/L. We demonstrate that DLS is a powerful technique to study the kinetics of destabilization of double emulsions.