Hydrological models are typically calibrated with discharge time series derived from a rating curve, which is subject to parametric and structural uncertainties that are usually neglected. In this work, we develop a Bayesian approach to probabilistically represent parametric and structural rating curve errors in the calibration of hydrological models. To achieve this, we couple the hydrological model with the inverse rating curve yielding the rainfall–stage model that is calibrated in stage space. Acknowledging uncertainties of the hydrological and the rating curve models allows assessing their contribution to total uncertainties of stages and discharges. Our results from a case study in France indicate that (a) ignoring rating curve uncertainty leads to changes in hydrological parameters, and (b) structural uncertainty of hydrological model dominates other uncertainty sources. The paper ends with discussing key challenges that remain to be addressed to achieve a meaningful quantification of various uncertainty sources that affect hydrological model, as including input errors.