  We construct a model describing the response of a hybrid system where the
electromagnetic field - in particular, surface plasmon polaritons - couples
strongly with electronic excitations of atoms or molecules. Our approach is
based on the input-output theory of quantum optics, and in particular it takes
into account the thermal and quantum vibrations of the molecules. The latter is
described within the $P(E)$ theory analogous to that used in the theory of
dynamical Coulomb blockade. As a result, we are able to include the effect of
the molecular Stokes shift on the strongly coupled response of the system. Our
model then accounts for the asymmetric emission from upper and lower polariton
modes. It also allows for an accurate description of the partial decoherence of
the light emission from the strongly coupled system. Our results can be readily
used to connect the response of the hybrid modes to the emission and
fluorescence properties of the individual molecules, and thus are relevant in
understanding any utilization of such systems, like coherent light harvesting.
