Context. The emission from Herbig-Haro objects and supersonic molecular outflows is understood as cooling radiation behind shocks, which are initiated by a (proto-)stellar wind or jet. Within a given object, one often observes both dissociative (J-type) and non-dissociative (C-type) shocks, owing to the collective effects of internally varying shock velocities. Aims: We aim at the observational estimation of the relative contribution to the cooling by CO and H2O, as this provides decisive information for understanding the oxygen chemistry behind interstellar shock waves. Methods: The high sensitivity of HIFI, in combination with its high spectral resolution capability, allowed us to trace the H2O outflow wings at an unprecedented signal-to-noise ratio. From the observation of spectrally resolved H2O and CO lines in the HH52-54 system, both from space and from the ground, we arrived at the spatial and velocity distribution of the molecular outflow gas. Solving the statistical equilibrium and non-LTE radiative transfer equations provides us with estimates of the physical parameters of this gas, including the cooling rate ratios of the species. The radiative transfer is based on an accelerated lambda iteration code, where we use the fact that variable shock strengths, distributed along the front, are naturally implied by a curved surface. Results: Based on observations of CO and H2O spectral lines, we conclude that the emission is confined to the HH54 region. The quantitative analysis of our observations favours a ratio of the CO-to-H2O-cooling-rate ≫1. Formally, we derived the ratio Lambda(CO)/Lambda(o-H2O) = 10, which is in good agreement with earlier determination of 7 based on ISO-LWS observations. From the best-fit model to the CO emission, we arrive at an H2O abundance close to 1 × 10-5. The line profiles exhibit two components, one that is triangular and another that is a superposed, additional feature. This additional feature is likely to find its origin in a region that is smaller than the beam where the ortho-water abundance is smaller than in the quiescent gas. Conclusions: Comparison with recent shock models indicate that a planar shock cannot easily explain the observed line strengths and triangular line profiles. We conclude that the geometry can play an important role. Although abundances support a scenario where J-type shocks are present, higher cooling rate ratios are derived than predicted by these types of shocks. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. Complementary observations were made with the following. Odin is a Swedish-led satellite project funded jointly by the Swedish National Space Board (SNSB), the Canadian Space Agency (CSA), the National Technology Agency of Finland (Tekes), and Centre National d'Étude Spatiale (CNES). The Swedish ESO Submillimetre Telescope (SEST) located at La Silla, Chile was funded by the Swedish Research Council (VR) and the European Southern Observatory. It was decommissioned in 2003. The Atacama Pathfinder EXperiment (APEX) is a collaboration between the Max-Planck-Institut für Radioastronomie, the European Southern Observatory and the Onsala Space Observatory.