Rare-earth iron garnet epitaxial films famous for their unique magnetic, microwave and optical properties consistently attract high interest. Domain structure of both bulk and interfaces of garnet films is closely connected with their magnetic properties and magnetization dynamics. In this work, we investigate the magnetic behaviour and domain structure of an epitaxial bismuth-substituted lutetium iron garnet film with a regular array of planar submicron particles made of Co film or Co/Pt multilayer on its surface. Optical polarization microscopy and magnetic force microscopy techniques used for the characterization of these composite structures confirm the mutual influence of the garnet and metal nanostructured layers on each other. On the one hand, dense ordered metal particles provide the pinning of the surface magnetic domains of the garnet film, which further affects the organization of the bulk stripe domains. On the other hand, we observed that the domain structure in the metallic pattern is governed by the domain structure of the garnet placed beneath it.