We report on the nature of the resonant modes in organic planar microcavities featuring semi-transparent metallic layers. We theoretically demonstrate that symmetric microcavities support a total of four modes originating from the coupling of surface plasmon polaritons. For red top-emitting organic light-emitting diodes with one semi-transparent metallic electrode, we identify three coupled plasmonic modes and calculate a light outcoupling efficiency close to 34% when assuming emitters with isotropic transition dipole moment. This value is estimated to increase to 50% in the case the dipole moment is purely horizontal.