Sequel to the fact that hybrid nanofluidic systems (e.g. scalable micro-/nanofluidic device) exhibit greater thermal resistance with increasing nanoparticle concentration, little is known on the significance of thermal radiation, surface roughness and linear stability of water conveying alumina and copper oxide nanoparticles. This study presents the effects of thermal radiation and surface roughness on the complex dynamics of water conveying alumina and copper oxide nanoparticles, in the case where the thermophysical properties of the resulting mixture vary meaningfully with the volume fraction of solid nanomaterials, as well as with the Brownian motion and thermophoresis microscopic phenomena. Based on the linear stability theory and normal mode analysis method, the basic partial differential equations governing the transport phenomenon were non-dimensionalized to obtain the simplified stability equations. The optimum values of the critical thermal Rayleigh number depicting the onset of thermo-magneto-hydrodynamic instabilities were obtained using the power series method and the Chock–Schechter numerical integration. The increase in the strength of Lorentz forces, thermal radiation and surface roughness has a stronger stabilizing impact on the appearance of convection cells. On the contrary, the stability diminishes with the increasing values of the volumetric fraction and diameter of nanomaterials. The partial substitution of the alumina nanoparticles by the copper oxide nanomaterials in the mixture stabilizes importantly the hybrid nanofluidic medium.