We investigate the interparticle interactions, phase behavior, and structure of microsphere-nanoparticle mixtures that possess high size and charge asymmetry. We employ a novel Monte Carlo simulation scheme to calculate the effective microsphere interactions in suspension, yielding new insight into the origin of the experimentally observed behavior. The initial settling velocity, final sediment density, and three-dimensional structure of colloidal phases assembled from these binary mixtures via gravitational settling of silica microspheres in water and index-matched solutions exhibit a strong compositional dependence. Confocal laser scanning microscopy is used to directly image and quantify their structural evolution during assembly. Below a lower critical nanoparticle volume fraction (phi(nano) < phi(L,C)), the intrinsic van der Waals attraction between microspheres leads to the formation of colloidal gels. These gels exhibit enhanced consolidation as phi(nano) approaches phi(L,C). When phi(nano) exceeds phi(L,C), an effective repulsion arises between microspheres due to the formation of a dynamic nanoparticle halo around the colloids. From this stable fluid phase, the microspheres settle into a crystalline array. Finally, above an upper critical nanoparticle volume fraction (phi(nano) > phi(U,C)), colloidal gels form whose structure becomes more open with increasing nanoparticle concentration due to the emergence of an effective microsphere attraction, whose magnitude exhibits a superlinear dependence on phi(nano).