Pedotransfer functions (PTFs) are widely used to estimate soil hydraulic properties (SHPs) from easily measurable characteristics. However, most existing PTFs rely on unimodal hydraulic models, which fail to accurately represent the bimodal SHPs caused by soil structure common in field conditions. In this study, we developed new PTFs using two bimodal soil hydraulic models and introduced soil physics-informed neural networks (SPINN) to embed the models into PTF training. The results showed that the new PTFs effectively captured bimodality in hydraulic conductivity curves, achieving an RMSE of 0.578 in the test set, compared to 0.709 for unimodal models. The PTFs also improved soil water retention curve (SWRC) predictions but struggled with bimodal SWRCs for some samples, likely due to the limited number of bimodal SWRCs in the dataset. An independent dataset evaluation revealed that the RMSE for hydraulic conductivity predicted by the new PTFs was approximately one-third of that of classic PTFs. This underscores the significant role of soil structure in SHPs, which classic PTFs fail to capture. Additionally, PTFs developed using the SPINN method outperformed those optimized fitted hydraulic parameters via machine learning, a common approach in the literature. We also found that separate versus simultaneous optimization of water retention and hydraulic conductivity greatly affects PTF performance. Finally, we provided global 1 km-resolution maps of soil hydraulic parameters for the bimodal model.