  We report an inelastic neutron scattering study on the spin resonance in the
bilayer iron-based superconductor CaKFe$_4$As$_4$. In contrast to its
quasi-two-dimensional electron structure, three strongly $L$-dependent modes of
spin resonance are found below $T_c=35$ K. The mode energies are below and
linearly scale with the total superconducting gaps summed on the nesting hole
and electron pockets, essentially in agreement with the results in cuprate and
heavy fermion superconductors. This observation supports the sign-reversed
Cooper pairing mechanism under multiple pairing channels and resolves the
long-standing puzzles concerning the broadening and dispersive spin resonance
peak in iron pnictides. More importantly, the triple resonant modes can be
classified into odd and even symmetries with respect to the distance of Fe-Fe
planes within the Fe-As bilayer unit. Thus, our results closely resemble those
in the bilayer cuprates with nondegenerate spin excitations, suggesting that
these two high-$T_c$ superconducting families share a common nature.
