By combining Brillouin light scattering and micromagnetic simulations, we studied the spin-wave (SW) dynamics of a Co/Pd thin film multilayer, which features a stripe domain structure at remanence. The periodic up and down domains are separated by corkscrew type domain walls. The existence of these domains causes a scattering of the otherwise bulk and surface SW modes, which form mode families, similar to a one-dimensional magnonic crystal. The dispersion relation and mode profiles of SWs are measured for the transferred wave vector parallel and perpendicular to the domain axis.