Wetland-dominated watersheds, such as those in the Prairie Pothole Region (PPR), contain numerous land depressions, contributing to their hydrological complexity. Overland flow generation in these regions follows the ‘fill-and-spill’ mechanism, where water fills wetlands until reaching spill capacity, then spills over and connects to the downstream river system. This behavior leads to a complex dynamic of the river network and watershed-scale hydrological behavior. Conventional models, assuming a temporally constant river network and contributing area, may not capture this complexity. Recent studies suggested a probabilistic approach to incorporate pothole storage capacities, and the dynamic of the fill-and-spill mechanism, within the algorithm of conventional conceptual models. Furthermore, researchers have recently begun coupling deep learning models, such as Long Short-Term Memory (LSTM), with conceptual models like HBV to simultaneously leverage the high performance of LSTM and the interpretability of HBV. This study uses the probabilistic concept and adds a new pothole module to HBV to represent the pothole storage complexities. The extended model is then coupled with LSTM to leverage the unprecedented optimization capability of LSTM. The developed model is explored along hundreds of undammed catchments within PPR with recorded streamflow observations from 1985 to 2020. The preliminary results show a stronger performance compared to conventional HBV models. Moreover, our learnable process-based model can simulate other untrained physical variables and fluxes, such as pothole storage, baseflow, and evapotranspiration, which can be explored to evaluate the physical realism of the developed model and to discover new patterns and hydrological functions relevant to wetland hydrology.