A dichroic structure consisting of two parallel arrays of crossed dipoles supported by various dielectric sheets is investigated. An efficient analysis method, based on a modal expansion that takes into account the interaction of the reactive field between the gratings, is outlined for this purpose. The method uses a Galerkin procedure combined with a generalised wave-matrix formulation. The analysis method is also implemented in a systematic design procedure, and the design of a double-layer grating structure intended for a dichroic subreflector operating at 10.7–11.7 GHz and 18.1–20.1 GHz is carried out.