We extend the multiple scattering formalism of Shettle and Green using a turbid atmosphere of uniform horizontal layers with vertical nonhomogeneities by introducing uniform cloud, haze, and smog layers. Our solution follows the rigorous equations of Chandrasekhar. The fact that it is capable of handling a cloud layer of large optical thickness with minimal subdivision of that layer permits a fast computer solution. A formalism for treating a fractional cloud layer is presented, and this allows the interesting possibility of an increase in the global flux over the clear-sky case that was not allowed by the uniform layers. The uv spectral and dose results are then compared with existing experimental data, and averaged effects are presented and parameterized.