While the catchment-scale stream-hillslope continuum is increasingly understood as a key determinant of land surface water/energy balances, the Earth System Model (ESM) community still lacks a proper hydrologic framework to capture water/energy exchanges in vertical and lateral directions between the unsaturated soil, saturated groundwater, and river/stream. To fill this gap, we develop a new modeling framework Soil, Hillslope Aquifer, and River Continuum (SHARC) integrated with the Geophysical Fluid Dynamics Laboratory (GFDL) Land Model (LM4). The LM4.1-SHARC employs the Boussinesq approximation to represent lateral groundwater fluxes and enables 1) accounting for the local horizontal hydraulic gradient between the riparian zone and stream as the driver of the stream-hillslope exchanges and 2) characterization of the hillslope aquifer based on its effective parameters (e.g., hydraulic diffusivity, and bedrock slope) through the method of streamflow recession analysis (i.e., hydraulic groundwater theory). We apply the LM4.1-SHARC model to the Pr ovidence headwater catchment at Southern Sierra, NV, and compare the model simulations with the available in-situ observations, including soil moisture, temperature, and baseflow. As a proof of concept, we show that the catchment-scale hillslope aquifer can be optimized, in terms of flux accuracy of soil drainage (vertical) and baseflow (lateral), by tuning the groundwater diffusivity and slope. In addition to the demonstration of enhanced water/energy budget simulations, we investigate the implications of a more comprehensive treatment of continuum processes such as impeded/facilitated soil drainage due to the stream-groundwater interactions to anthropogenic warming on a decadal to century scale.