Stream-groundwater interactions are crucial for the stream and surrounding ecosystem conservation, which also have a great impact on sustainable water resources utilization and water environment protection. To address the limitations of previous studies in locating the free surface at the water table, this paper adopts the Boussinesq equation as the governing equation to construct a stream-groundwater interaction model located at the air entry plane. Laplace transform is used to obtain the analytical solution of the model, and a corresponding parameter inversion model is constructed in the meantime. By comparing the analytical solution with the numerical solution of saturated-unsaturated seepage, the validity of the proposed model is verified. Subsequently, a parameter sensitivity analysis is conducted to investigate the variations in air entry plane elevation. The calculation method and distinctive features of vertical velocity at the air entry plane are discussed based on the seepage continuity equation and water balance relationship. The findings demonstrate that the Boussinesq stream-groundwater interaction model is in excellent agreement with the numerical solution, thereby validating the effectiveness of the modified model. In contrast to previous models, the model addresses the limitations associated with the free surface at the water table, providing a more robust theoretical foundation and more logical physical interpretations of the parameters.