We consider the filtration combustion for configuration where air is injected behind the wave into a porous medium containing a solid fuel. The simplest flow contains planar combustion and thermal waves, each propagating with its own speed. In this work, we study such a flow, in the case where the porous medium contains initially also some amount of liquid; therefore, vaporization and condensation occur too, giving rise to a wave structure richer than in dry combustion. We find two possible sequences of waves, and we characterize the internal structure of all waves. In an example for typical parameters of in-situ combustion, we compare the analytical results with direct numerical simulations.