We experimentally demonstrate the enhancement of the far-field thermal radiation between two nonabsorbent Si microplates coated with energy-absorbent silicon dioxide (SiO_{2}) nanolayers supporting the propagation of surface phonon polaritons. By measuring the radiative thermal conductance between two coated Si plates, we find that its values are twice those obtained without the SiO_{2} coating. This twofold increase results from the hybridization of polaritons with guided modes inside Si and is well predicted by fluctuational electrodynamics and an analytical model based on a two-dimensional density of polariton states. These findings could be applied to thermal management in microelectronics, silicon photonics, energy conversion, atmospheric sciences, and astrophysics.