Context. Monoceros R2 (Mon R2), at a distance of 830 pc, is the only ultra-compact H ii region (UC H ii) where its associated photon-dominated region (PDR) can be resolved with the Herschel Space Observatory. Aims: Our aim is to investigate observationally the kinematical patterns in the interface regions (i.e., the transition from atomic to molecular gas) associated with Mon R2. Methods: We used the HIFI instrument on board Herschel to observe the line profiles of the reactive ions CH+, OH+, and H2O+ toward different positions in Mon R2. We derive the column density of these molecules and compare them with gas-phase chemistry models. Results: The reactive ion CH+ is detected both in emission (at central and red-shifted velocities) and in absorption (at blue-shifted velocities). The OH+ ion is detected in absorption at both blue- and red-shifted velocities, with similar column densities; H2O+ is not detected at any of the positions, down to a rms of 40 mK toward the molecular peak. At this position, we find that the OH+ absorption originates in a mainly atomic medium, and therefore is associated with the most exposed layers of the PDR. These results are consistent with the predictions from photo-chemical models. The line profiles are consistent with the atomic gas being entrained in the ionized gas flow along the walls of the cavity of the H ii region. Based on this evidence, we are able to propose a new geometrical model for this region. Conclusions: The kinematical patterns of the OH+ and CH+ absorption indicate the existence of a layer of mainly atomic gas for which we have derived, for the first time, some physical parameters and its dynamics. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.