Soil hydraulic properties (SHPs) are impacted by various mechanisms such as soil structure, capillarity, and adsorption forces, often showing a bimodal shape. Developing soil hydraulic models that describe SHPs over the entire saturation range often involves balancing the representation of multiple processes while minimizing the number of free-fitted parameters. Existing soil hydraulic models rarely capture bimodal soil hydraulic properties across the full moisture range or introduce too many free-fitted parameters. In this study, we propose a novel framework to describe SHPs over the entire moisture range, accounting for the effects of soil structure, capillarity, adsorption forces, and vapor diffusion. In its four free-fitted parameters form, the proposed models can capture unimodal soil water retention curves (SWRC) and bimodal hydraulic conductivity curves (HCC). With one additional free-fitted parameter, the proposed models can capture both bimodal SWRC and HCC. Testing with 107 and 52 soil samples from two public datasets demonstrated that the proposed models performed exceptionally well in describing SHPs across the entire moisture range. The reported lowest root-mean-square error values were 0.005 and 0.009 cm3 cm−3 for fitting SWRCs, and 0.465 and 0.666 for predicting HCCs, respectively. Due to the minimal introduction of free-fitted parameters, the proposed framework showed significant application potential.