Generalized Snell-Descartes and Fresnel laws are derived for harmonic inhomogeneous plane waves that are incident upon a static interface between two continuous absorbing dielectric media that are macroscopically characterized by their electric and magnetic permittivities and their conductivities. A coordinate-free formalism based on complex vector algebra is used to carry out all discussions. Surprisingly, the usual complex Snell-Descartes laws for reflection and refraction and Fresnel laws for polarization are recovered only in the special case in which the vector characterizing the direction of inhomogeneity is in the plane of incidence. In the more general case a new deflection angle between planes of incidence and refraction has to be introduced. An experiment is proposed to test this prediction. A generalized form of the TE and TM modes (with respect to the interface), which are elliptically polarized and which are called parallel electric and parallel magnetic modes, also emerges.