We present 3D Surface Splatting (3DSS), the first differentiable surface splatting renderer for physically-based inverse rendering from multi-view images. Our central insight is that the surface separation problem at the heart of surface splatting admits a direct formulation in terms of the reconstruction kernels themselves. From this foundation we derive a coverage-based compositing model whose per-layer opacity arises directly from the accumulated Elliptical Weighted Average reconstruction weight, yielding anti-aliased silhouettes and informative visibility gradients at sparsely covered edges. Combined with forward microfacet shading under co-optimized HDR environment lighting and density-aware adaptive refinement, 3DSS jointly recovers shape, spatially-varying BRDF materials, and illumination. Because the optimized representation is a set of oriented surface samples, it bridges natively to mesh-based workflows via surface reconstruction from oriented point cloud methods. We evaluate 3DSS against mesh-based, implicit, and Gaussian-splatting baselines across geometry reconstruction, novel-view synthesis, and novel-illumination relighting.