We report on experimental observations of self-assemblies in colloidal dispersions of clay nanoplatelets and magnetic nanoparticles. Visual observations have been combined with small angle X-ray scattering (SAXS) in the study of several composites at a fixed clay concentration in the dilute regime, and varying ferrofluid concentrations. Our visual observations which encompass macroscopic separation in gravitational- and magnetic field, indicate that all samples present a concentrated phase and a diluted one. SAXS data obtained from each phase are consistent with the interpretation that the scattering contribution from the clay nano-platelets in the samples can be neglected in comparison with the magnetic particle contribution. The analysis of the scattered intensity is performed combining two models, one based on the global scattering function and the other allowing the extraction of the structure factor of the mixtures. The parameters of the size distribution of magnetic nanoparticles determined by both methods are in good agreement. The structure factor of the mixtures shows that on a local scale, the mixtures behave like a gas of isolated magnetic nanoparticles. It also indicates the presence of interactions between magnetic nanoparticles mediated by the presence of Laponite platelets. Such interactions could be attributed with a progressive partial phase separation between spheres and discs rather than to the formation of dense aggregates.