A rigorous theoretical treatment to analyze the electromagnetic scattering of an inhomogeneous elliptically polarized plane wave by a sphere buried in a lossy half-space is presented. To consider the losses in the media an inhomogeneous plane wave is considered. The incident and the scattered electric field components are expanded in series of vectorial spherical harmonics using the Legendre functions generalized via hypergeometrical and gamma functions, with unknown expansion coefficients. The spectral-domain method to represent the scattered electric field is used in order to compute the scattered-reflected and scattered-transmitted fields, considering the reflection and transmission of each elementary plane wave by the interface. Finally, the unknown coefficients of the scattered field are computed by imposing the boundary condition on the spherical surface. In order to validate the model, a homemade code has been implemented. Comparisons with the simulations performed with a commercial software and the results in the literature are presented.