A plane wave impinges on a laterally double-periodic inhomogeneous lossy dielectric structure. Using a wave splitting approach, and an expansion of the fields and permittivity in entire domain basis functions, the scattered fields are determined via a propagator. The formulation is originally intended for constitutive parameters which vary continuously but is here applied to structures with an abruptly varying permittivity. The method resembles the so called coupled-wave analysis method. Calculated results are compared with experimental data for a slab with domains of a piecewise homogeneous permittivity. The agreement is good considering the error sources in the experiment. The results are compared with calculated results obtained by an entirely different method showing very good agreement for the examples given. The method is also used on a pyramidal absorber-like structure.