The problem of diffuse reflection and transmission of the solar radiation by the earth's atmosphere is discussed taking into account the effects of polarization and inhomogeneity of the atmosphere. Firstly, we discuss the formulation of basic equations for the reflection and transmission matrices which describe the intensity and state of polarization of the diffusely reflected and transmitted radiation. Some revisions on the equations for a homogneous atmosphere derived by Chandrasekhar and Sekera have been made. The symmetry relationships for the reflection and transmission matrices are also examined and presented in a more general form than that given by Hovenier. We then develop a method for the numerical solution by extending the matrix method proposed by Towmey et al. to include the effects of polarization and inhomogeneity of the atmosphere. After some modifications of the reflection and transmission matrices, algebraic equations satisfied by these modified matrices are derived. These derived equations enable us to compute the properties of thick layers by building them up from thinner sublayers. Discussion is also made on reduction of the solution from that of the problem with underlying surface which reflects the incident radiation to that of the standard problem without reflecting surface.