We present a combined experimental and numerical study of the spin-wave dispersion in a NiFe artificial spin-ice (ASI) system consisting of an array of stadium-shaped nanoislands deposited on the top of a continuous NiFe film with non-magnetic spacer layers of varying thickness. The spin-wave dispersion, measured by wavevector resolved Brillouin light scattering spectroscopy in the Damon–Eshbach configuration, consists of a rich number of modes, with either stationary or propagating character. We find that the lowest frequency mode displays a bandwidth of ∼0.5 GHz, which is independent of the presence of the film underneath. On the contrary, the Brillouin light scattering intensity of some of the detected modes strongly depends on the presence of the extended thin-film underlayer. Micromagnetic simulations unveil the details of the dynamic coupling between the ASI lattice and film underlayer. Interestingly, the ASI lattice facilitates dynamics of the film either specific wavelengths or intensity modulation peculiar to the modes of the ASI elements imprinted in the film. Our results demonstrate that propagating spin waves can be modulated at the nanometer length scale by harnessing the dynamic mode coupling in the vertical, i.e., the out-of-plane direction of suitably designed magnonic structures.