We characterize strongly coupled microcavities in which optical hybridization occurs between the organic-dye zinc tetraphenyl-porphrin (ZnTPP) and a thin film of a self-assembled perovskite. Position-resolved reflectivity measurements demonstrate the formation of hybrid organic-inorganic exciton polaritons corresponding to a three-way admixture of the cavity photon with the electronic transitions of the ZnTPP and the perovskite. We find that such hybrid-polariton states can undergo radiative emission, despite the existence of a competing decay channel to lower-lying $Q$-band states. We argue that such hybrid polaritons can in principle act as an intermediate energy-transfer state between the organic and inorganic excitations.