We report a survey of the magnetic properties of metal-organic complexes coupled to ferromagnetic and antiferromagnetic surfaces. Using element-resolved X-ray magnetic circular dichroism, we investigate the magnetism of single, double, and triple-decker phthalocyanines focusing on MnPc, TbPc2, and Tb2Pc3 deposited on Ni, Mn, and CoO thin films. Depending on the number of Pc ligands, we find that the metal ions within the molecules couple either parallel or antiparallel to a ferromagnetic substrate. Whereas single-decker complexes such as MnPc form a unique magnetic entity with ferromagnetic films, the intrinsic single molecule magnet properties of TbPc2 and Tb2Pc3 remain largely unaltered. TbPc2 deposited on perpendicularly magnetized Ni films exhibits enhanced magnetic stability compared to TbPc2 in molecular crystals, opposite to TbPc2 deposited on in-plane magnetized Ni. Depending on the competition between uniaxial anisotropy, superexchange, and Zeeman interaction, the magnetic moment of TbPc2 can be aligned parallel or antiparallel to that of the substrate by modulating the intensity of an external magnetic field. This occurs also for Tb2Pc3, but the substrate-induced exchange coupling in triple-decker molecules is found to be short-ranged, that is, limited to the Tb ion closer to the ferromagnetic surface. Finally, we discuss the conditions required to establish exchange bias between molecules and antiferromagnetic substrates. We show that TbPc2 deposited on antiferromagnetic Mn thin films exhibits both exchange bias and enhanced coercivity when field cooled parallel to the out-of-plane easy axis. However, exchange bias does not extend to all molecules on the surface. On oxide antiferromagnets such as CoO we find no evidence of exchange bias for either TbPc2 or MnPc. ; We received financial support from the European Research Council (StG 203239 NOMAD), the Ministerio de Ciencia e Innovación (MAT2010-15659), the Agència de Gestió d'Ajuts Universitaris i de Recerca (2009 SGR 695), and the Swiss Competence Centre for Materials Science and Technology (CCMX). ; Peer Reviewed