Summary Interactions between surface water and groundwater play an essential role in hydrology, hydrogeology, ecology, and water resources management. A proper characterisation of riverbed structures might be important for estimating river–aquifer exchange fluxes. The ensemble Kalman filter (EnKF) is commonly used in subsurface flow and transport modelling for estimating states and parameters. However, EnKF only performs optimally for MultiGaussian distributed parameter fields, but the spatial distribution of streambed hydraulic conductivities often shows non-MultiGaussian patterns, which are related to flow velocity dependent sedimentation and erosion processes. In this synthetic study, we assumed a riverbed with non-MultiGaussian channel-distributed hydraulic parameters as a virtual reference. The synthetic study was carried out for a 3-D river–aquifer model with a river in hydraulic connection to a homogeneous aquifer. Next, in a series of data assimilation experiments three different groups of scenarios were studied. In the first and second group of scenarios, stochastic realisations of non-MultiGaussian distributed riverbeds were inversely conditioned to state information, using EnKF and the normal score ensemble Kalman filter (NS-EnKF). The riverbed hydraulic conductivity was oriented in the form of channels (first group of scenarios) or, with the same bimodal histogram, without channelling (second group of scenarios). In the third group of scenarios, the stochastic realisations of riverbeds have MultiGaussian distributed hydraulic parameters and are conditioned to state information with EnKF. It was found that the best results were achieved for channel-distributed non-MultiGaussian stochastic realisations and with parameter updating. However, differences between the simulations were small and non-MultiGaussian riverbed properties seem to be of less importance for subsurface flow than non-MultiGaussian aquifer properties. In addition, it was concluded that both EnKF and NS-EnKF improve the characterisation of non-MultiGaussian riverbed properties, hydraulic heads and exchange fluxes by piezometric head assimilation, and only NS-EnKF could preserve the initial distribution of riverbed hydraulic conductivities.