We present evidence for “image biexcitons” within organic-inorganic perovskite-coated silver gratings. These composite quasiparticles are formed by the interaction between an exciton and its image in the metal mirror below, with binding energy 100 meV at room temperature. By changing the polar and azimuthal angles of the incident light, we observe strong coupling between excitons and surface plasmon polaritons on the grating, with Rabi splittings of 150 and 125 meV for the exciton and biexciton, respectively. A detailed analysis of the field polarizations and dipole orientations shows how these Rabi couplings arise from the strongly compressed field volume.