Novel view synthesis for underwater scene reconstruction presents unique challenges due to complex light-media interactions. Optical scattering and absorption in water body bring inhomogeneous medium attenuation interference that disrupts conventional volume rendering assumptions of uniform propagation medium. While 3D Gaussian Splatting (3DGS) offers real-time rendering capabilities, it struggles with underwater inhomogeneous environments where scattering media introduces artifacts and inconsistent appearance. In this study, we propose a physics-based framework that disentangles object appearance from water medium effects through tailored Gaussian modeling. Our approach introduces appearance embeddings, which are explicit medium representations for backscatter and attenuation, enhancing scene consistency. In addition, we propose a depth-guided optimization strategy that leverages pseudo-depth maps as supervision with depth regularization and scale penalty terms to improve geometric fidelity. By integrating the proposed appearance and medium modeling components via an underwater imaging model, our approach achieves both high-quality novel view synthesis and physically accurate scene restoration. Experiments demonstrate our significant improvements in rendering quality and restoration accuracy over existing methods. The project page is available at https://bilityniu.github.io/3D-UIR.