Anderson localization simulations in one-dimensional disordered optical systems usually focus on the localization length or its inverse, but the calculation of the density of states has appeared less frequently for such models. In this paper a technique originally used to calculate the integrated density of states for one-dimensional disordered crystals supporting electron propagation is modified for use with randomly layered optical media. The density of states is then readily available via differentiation. The algorithm is demonstrated on one-dimensional quarter-wave stack and non-quarter-wave stack models with layer thicknesses disordered.