Camera-based 3D Semantic Scene Completion (SSC) is a critical task in autonomous driving systems, assessing voxel-level geometry and semantics for holistic scene perception. While existing voxel-based and plane-based SSC methods have achieved considerable progress, they struggle to capture physical regularities for realistic geometric details. On the other hand, neural reconstruction methods like NeRF and 3DGS demonstrate superior physical awareness, but suffer from high computational cost and slow convergence when handling large-scale, complex autonomous driving scenes, leading to inferior semantic accuracy. To address these issues, we propose the Semantic-PHysical Engaged REpresentation (SPHERE) for camera-based SSC, which integrates voxel and Gaussian representations for joint exploitation of semantic and physical information. First, the Semantic-guided Gaussian Initialization (SGI) module leverages dual-branch 3D scene representations to locate focal voxels as anchors to guide efficient Gaussian initialization. Then, the Physical-aware Harmonics Enhancement (PHE) module incorporates semantic spherical harmonics to model physical-aware contextual details and promote semantic-geometry consistency through focal distribution alignment, generating SSC results with realistic details. Extensive experiments and analyses on the popular SemanticKITTI and SSCBench-KITTI-360 benchmarks validate the effectiveness of SPHERE. The code is available at https://github.com/PKU-ICST-MIPL/SPHERE_ACMMM2025.