The coupled groundwater-surface water model is an essential tool for quantitatively characterizing the interactions between groundwater and surface water as well as hydrological processes in watersheds. With the rise of artificial intelligence, data-driven machine learning methods have made significant advancements in the field of surface water or groundwater simulation, overcoming challenges faced by traditional hydrological numerical models. However, a data-driven groundwater-surface water coupling model that simultaneously predicts both surface runoff and groundwater levels has not been observed thus far. By combining multitask Convolutional Neural Networks (CNN) and Long Short-Term Memory (LSTM) neural networks, this study construct a data-driven coupled model for the Sagehen watershed, simultaneously predicting river runoff and groundwater levels. The results indicate that the deep learning model established on CNN and LSTM achieves a Nash-Sutcliffe Efficiency coefficient (NSE) of 0.8094 for simulating surface runoff and an NSE higher than 0.81 for simulating groundwater levels in the study area, demonstrating satisfactory simulation performance. The findings of this research offer new insights into watershed groundwater-surface water coupling simulation, thereby contributing to the advancement of this field.