The magnetic and superconducting properties of epitaxial, (100)-oriented GdN/W/NbN/W multilayers have been characterized. We find that the interfacial layer of W permits the GdN/NbN layers to be grown smoothly. We report large flux trapping effects in the magnetic hysteresis loops measured below the superconducting transition temperature (T-c) of the multilayer, indicating the coexistence of magnetism and superconductivity down to layer thicknesses of 40 and 22 Angstrom for the NbN and GdN, respectively. Nonmagnetic NbN/W multilayers were also studied; in these multilayers, T-c is enhanced considerably above that of a single NbN layer due to coupling of the superconducting layers across the W spacers. This behavior is fitted to a model which explicitly includes interlayer coupling. [S0021-8979(98)04014-6].