In this study, we investigate transmitted, reflected, and absorbed powers in forward and backward directions of periodic and aperiodic multilayered structures composed of bi-anisotropic metamaterial (MM) slab and conventional material. Aperiodic multilayered structure is realized by a change in thickness of any bi-anisotropic MM slab or of any conventional material. From this analysis, we note the following key results. First, identical (non-identical) forward and backward transmitted (reflected and absorbed) powers are observed for the analyzed periodic and aperiodic multilayered structures due to reciprocity (reflection-asymmetry) of bi-anisotropic MM slabs. Second, thickness-resonance phenomenon of conventional materials produces some pe...