We propose a novel method for determining the structural and thermodynamic properties of nanoparticle- protein complexes under physiological conditions. The method consists of collecting a full set of small-angle X-ray and neutron-scattering measurements in solutions with different concentrations of nanoparticles and protein. The nanoparticle-protein dissociation process is described in the framework of the Hill cooperative model, based on which the whole set of X-ray and neutron-scattering data is fitted simultaneously. This method is applied to water solutions of gold nanoparticles in the presence of human serum albumin without any previous manipulation and can be, in principle, extended to all systems. We demonstrate that the protein dissociation constant, the Hill coefficient, and the stoichiometry of the nanoparticle-protein complex are obtained with a high degree of confidence.