The conditions of splitting the reflectance, transmittance and absorption spectra of a dispersive symmetric Fabry-Perot microcavity are studied on the basis of classical multibeam interference formula, The special case of a monolithic semiconductor microcavity with quantum well excitons is studied in detail. The problem of resonant splitting of transmittance in the case of a single dispersive quantum well is solved exactly. A useful formalism including generalized time-invariance and well-suited for the analysis of composite stacks of absorbing dielectrics, especially when substructures exhibit spatial symmetries, is treated in the Appendix.