The presence of unsaturated zones at the river-aquifer interface has large implications on numerous hydraulic and chemical processes. However, the hydrological and geological controls that influence the development of unsaturated zones have so far only been analyzed with simplified conceptualizations of flow processes, or homogeneous conceptualizations of the hydraulic conductivity in either the aquifer or the riverbed. We systematically investigated the influence of heterogeneous structures in both the riverbed and the aquifer on the development of unsaturated zones. A stochastic 1-D criterion that takes both riverbed and aquifer heterogeneity into account was developed using a Monte Carlo sampling technique. The approach allows the reliable estimation of the upper bound of the spatial extent of unsaturated areas underneath a riverbed. Through systematic numerical modeling experiments, we furthermore show that horizontal capillary forces can reduce the spatial extent of unsaturated zones under clogged areas. This analysis shows how the spatial structure of clogging layers and aquifers influence the propensity for unsaturated zones to develop: In riverbeds where clogged areas are made up of many small, spatially disconnected patches with a diameter in the order of 1 m, unsaturated areas are less likely to develop compared to riverbeds where large clogged areas exist adjacent to unclogged areas. A combination of the stochastic 1-D criterion with an analysis of the spatial structure of the clogging layers and the potential for resaturation can help develop an appropriate conceptual model and inform the choice of a suitable numerical simulator for river-aquifer systems.