We have developed a simplified approach to fabricate high-reflectivity mirrors suitable for applications in a strongly-coupled organic-semiconductor microcavity. Such mirrors are based on a small number of quarter-wave dielectric pairs deposited on top of a thick silver film that combine high reflectivity and broad reflectivity bandwidth. Using this approach, we construct a microcavity containing the molecular dye BODIPY-Br in which the bottom cavity mirror is composed of a silver layer coated by a SiO₂ and a Nb₂O₅ film, and show that this cavity undergoes polariton condensation at a similar threshold to that of a control cavity whose bottom mirror consists of ten quarter-wave dielectric pairs. We observe, however, that the roughness of the hybrid mirror—caused by limited adhesion between the silver and the dielectric pair—apparently prevents complete collapse of the population to the ground polariton state above the condensation threshold.