The Good-Karali theory is extended to simulate composite circular dichroism (CD) through a cholesteric stack by incorporating chromophore's selective absorption (SA) and cholesteric stack's selective reflection (SR). Based on the independently evaluated anisotropic refractive indices and absorption coefficients, helical sense and pitch length, and film thickness, the theory is capable of describing transmission, reflection, and absorption through spin-cast cholesteric glassy liquid crystal films of nonafluorene. The resulting composite CD spectra agree quite well with experimental observations. The theory informs that SA plays a dominant role over SR in the composite CD. Specifically, the right-handed stack of the chromophore with its absorption dipole aligned with the local director in the cholesteric stack preferentially absorbs the left-handed over the right-handed circularly polarized light. The algebraic sign of the predicted composite CD flips by reversing the cholesteric host film's handedness without altering other parameter values. The established theory and computation constitute a solid foundation for optimizing circular polarizers by exploring the readily accessible parameter space targeting various potential applications.