Symmetry principles and theorems are of crucial importance in optics. Indeed, from one side, they allow obtaining direct insights into phenomena by eliminating unphysical interpretations; from the other side, they guide the designer of photonic components by narrowing down the parameter space of design variables. In this Letter, we illustrate a significant departure from the Babinet spectral complementarity in a very common and technologically relevant situation: that of a patterned conducting screen placed on a subwavelength dielectric slab. The symmetry property predicted by the Babinet theorem is correctly recovered for pairs of geometrically complementary-but less realistic in terms of applications-free-standing patterned screens. Our analysis merges experimental data with fully vectorial electromagnetic modeling and provides an alternative form of the Babinet theorem that highlights a connection with the concept of electromagnetic duality.