The two-dimensional excitons of transition metal dichalcogenide (TMDC) monolayers make these materials extremely promising for optical and optoelectronic applications. When the excitons interact with the electromagnetic field, they will give rise to exciton-polaritons, i.e., modes that propagate in the material plane while being confined in the out-of-plane direction. In this work, we derive the characteristic equations that determine both radiative and polaritonic modes in TMDC monolayers and we analyze the dispersion and decay rate of the modes. The condition for the existence of exciton-polaritons can be described in terms of a strong-coupling regime for the interaction between the exciton and the three-dimensional continuum of free-space electromagnetic modes. We show that the threshold for the strong-coupling regime critically depends on the interplay between nonradiative losses and the dielectric function imbalance at the two sides of the monolayer. Our results illustrate that a fine control of the dielectric function of the embedding media is essential for realizing exciton-polaritons in the strong-coupling regime.