  We provide a theoretical framework based on classical electromagnetism, to
describe optical properties of Fabry-P\'erot 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 reciprocity and
time-reversal symmetry constrain the modelling of such cavities. We apply this
approach to investigate numerically and analytically the properties of various
Fabry-P\'erot 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 mirrors interfaces. Our approach is
relevant for designing innovative Fabry-P\'erot cavities for chiral-sensing,
and for probing cavity-modified stereochemistry.
