Accurate and efficient prediction of spatiotemporal variations in the distribution of substances in fluids (SIFs) is crucial for various aspects of fluid mechanics related research and applications, involving for instance, material transport quantification, water quality assessment, and engineering condition analysis. This study proposes a framework for resolving the spatiotemporal distribution of SIFs such as salt and suspended sediment based on water levels and flow velocities. The framework incorporates a deep learning model based on a classic neural operator (DeepONet) architecture, which consists of a feature network and a position network to encode the characteristics of input variables and the problem domain. Numerical simulations were performed to generate the needed datasets. The framework was well-validated by predicting salinity and suspended sediment concentration (SSC) distributions in two idealized cases and a real-word case, demonstrating its efficacy and robustness. Time-series validation further demonstrated the prediction accuracy of the framework. The deep learning model is also capable of enhanced-resolution predictions, enabling the generation of high-resolution spatial distributions of SIFs from low-resolution hydrodynamic data. Both bottom and surface layers of the water column were analyzed, revealing that the mapping relationships between hydrodynamics and SIF distributions can be accurately captured throughout the water column, despite variations in correlation coefficients. Due to these capabilities and advantages, additional data sources can be integrated into the framework in the future, highlighting its considerable potential for broader applications in aquatic environments.