We investigate, both theoretically and experimentally, the wetting morphology of a liquid which is adsorbed onto a chemically structured substrate consisting of circular lyophobic domains in a lyophilic matrix. For thick films, the adsorbate morphology is not affected by the underlying domain pattern but reduction in the film thickness leads to the formation of stable holes and, thus, to perforated wetting films. These perforated films, which exist for an intermediate range of volumes, are bounded by surfaces of both constant mean curvature and high topological genus. By making use of nodoids, we are able to derive an approximate analytical parametrization of these surfaces. This "muffin-tin" parametrization captures the essential features of the wetting layer morphology as shown by comparison with direct numerical minimization of the free energy. Furthermore, the theoretical shapes are in very good agreement with experimental data obtained by atomic force microscopy.