We provide a theoretical framework based on classical electromagnetism to describe optical properties of Fabry-Pérot cavities filled with multilayered and linear chiral materials. We find a formal link between transfer-matrix, scattering-matrix, and Green-function approaches to compute the polarization-dependent optical transmission, and cavity-modified circular dichroism signals. We show how general symmetries like Lorentz's reciprocity and time-reversal symmetry constrain the modeling of such cavities. We apply this approach to investigate numerically and analytically the properties of various Fabry-Pérot cavities, made of either metallic or helicity-preserving dielectric photonic crystal mirrors. In the latter case, we analyze the onset of chiral cavity polaritons in terms of partial helicity preservation of electromagnetic waves reflected at the mirror interfaces. Our approach is relevant for designing innovative Fabry-Pérot cavities for chiral sensing and for probing cavity-modified stereochemistry.