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We propose a neural inverse rendering pipeline called IRON that operates on photometric images and outputs high-quality 3D content in the format of triangle meshes and material textures readily deployable in existing graphics pipelines. Our method adopts neural representations for geometry as signed distance fields (SDFs) and materials during optimization to enjoy their flexibility and compactness, and features a hybrid optimization scheme for neural SDFs: first, optimize using a volumetric radiance field approach to recover correct topology, then optimize further using edgeaware physics-based surface rendering for geometry refinement and disentanglement of materials and lighting. In the second stage, we also draw inspiration from mesh-based differentiable rendering, and design a novel edge sampling algorithm for neural SDFs to further improve performance. We show that our IRON achieves significantly better inverse rendering quality compared to prior works.