We have investigated the structure and magnetism of self-assembled, 20 nm diameter iron oxide nanoparticles covered by an oleic acid shell for scrutinizing their structural and magnetic correlations. The nanoparticles were spin-coated on an Si substrate as a single monolayer and as a stack of 5 ML forming a multilayer. X-ray scattering (reflectivity and grazing incidence small-angle scattering) confirms high in-plane hexagonal correlation and a good layering property of the nanoparticles. Using polarized neutron reflectivity we have also determined the long range magnetic correlations parallel and perpendicular to the layers in addition to the structural ones. In a field of 5 kOe we determine a magnetization value of about 80% of the saturation value. At remanence the global magnetization is close to zero. However, polarized neutron reflectivity reveals the existence of regions in which magnetic moments of nanoparticles are well aligned, while losing order over longer distances. These findings confirm that in the nanoparticle assembly the magnetic dipole-dipole interaction is rather strong, dominating the collective magnetic properties at room temperature.