A computational protocol for magneto-chiral dichroism and magneto-chiral birefringence dispersion is presented within the framework of damped response theory, also known as complex polarization propagator theory, at the level of time-dependent Hartree-Fock and time-dependent density functional theory. Magneto-chiral dichroism and magneto-chiral birefringence spectra in the (resonant) frequency region below the first ionization threshold of R-methyloxirane and L-alanine are presented and compared with the corresponding results obtained for both the electronic circular dichroism and the magnetic circular dichroism. The additional information content yielded by the magneto-chiral phenomena, as well as their potential experimental detectability for the selected species, is discussed.