Accurate, detailed, and regularly updated bathymetry, coupled with complex semantic content, is essential for under-mapped shallow-water environments facing increasing climatological and anthropogenic pressures. However, existing approaches that derive either depth or seabed classes from remote sensing imagery treat these tasks in isolation, forfeiting the mutual benefits of their interaction and hindering the broader adoption of deep learning methods. To address these limitations, we introduce Seabed-Net, a unified multi-task framework that simultaneously predicts bathymetry and pixel-based seabed classification from remote sensing imagery of various resolutions. Seabed-Net employs dual-branch encoders for bathymetry estimation and pixel-based seabed classification, integrates cross-task features via an Attention Feature Fusion module and a windowed Swin-Transformer fusion block, and balances objectives through dynamic task uncertainty weighting. In extensive evaluations at two heterogeneous coastal sites, it consistently outperforms traditional empirical models and traditional machine learning regression methods, achieving up to 75\% lower RMSE. It also reduces bathymetric RMSE by 10-30\% compared to state-of-the-art single-task and multi-task baselines and improves seabed classification accuracy up to 8\%. Qualitative analyses further demonstrate enhanced spatial consistency, sharper habitat boundaries, and corrected depth biases in low-contrast regions. These results confirm that jointly modeling depth with both substrate and seabed habitats yields synergistic gains, offering a robust, open solution for integrated shallow-water mapping. Code and pretrained weights are available at https://github.com/pagraf/Seabed-Net.