3D semantic scene completion (SSC) is an ill-posed task that requires inferring a dense 3D scene from incomplete observations. Previous methods either explicitly incorporate 3D geometric input or rely on learnt 3D prior behind monocular RGB images. However, 3D sensors such as LiDAR are expensive and intrusive while monocular cameras face challenges in modeling precise geometry due to the inherent ambiguity. In this work, we propose StereoScene for 3D Semantic Scene Completion (SSC), which explores taking full advantage of light-weight camera inputs without resorting to any external 3D sensors. Our key insight is to leverage stereo matching to resolve geometric ambiguity. To improve its robustness in unmatched areas, we introduce bird's-eye-view (BEV) representation to inspire hallucination ability with rich context information. On top of the stereo and BEV representations, a mutual interactive aggregation (MIA) module is carefully devised to fully unleash their power. Specifically, a Bi-directional Interaction Transformer (BIT) augmented with confidence re-weighting is used to encourage reliable prediction through mutual guidance while a Dual Volume Aggregation (DVA) module is designed to facilitate complementary aggregation. Experimental results on SemanticKITTI demonstrate that the proposed StereoScene outperforms the state-of-the-art camera-based methods by a large margin with a relative improvement of 26.9% in geometry and 38.6% in semantic.