We discuss the use of Mueller matrices for characterizing the reflecting properties of beetles, including matching patterns of significant elements to specific cuticular architectures. In the case of illumination by natural light, the parameters of the reflected light are related to the elements of the first column of the matrix. The green and red beetle Stephanorrhina guttata is shown to be a narrowband polarization-preserving reflector apart from depolarizing white patches, the green Calloodes grayanus a narrowband left-circular reflector, and the gold Anoplognathus parvulus behaves as a broadband left-circular reflector. Comparison of experimental and simulated matrices confirms that the beetle reflectors are natural analogs of all-dielectric thin-film reflectors. However, the gold Chrysina resplendens, which was formerly known as Plusiotis resplendens and reflects both right-handed and left-handed light, is represented by an ensemble of laterally incoherent chiral thin-film reflectors.