Superlattices of (LaMnO3)2n/(SrMnO3)n (n=1 to 5), composed of the insulators LaMnO3 and SrMnO3, undergo a metal-insulator transition as a function of n, being metallic for n<=2 and insulating for n>=3. Measurements of transport, magnetization and polarized neutron reflectivity reveal that the ferromagnetism is relatively uniform in the metallic state, and is strongly modulated in the insulating state, being high in LaMnO3 and suppressed in SrMnO3. The modulation is consistent with a Mott transition driven by the proximity between the (LaMnO3)/(SrMnO3) interfaces. Disorder localizes states at the Fermi level at the interfaces for n>=3. We suggest that this disorder is due to magnetic frustration at the interfaces.