The integration of hyperspectral (HS) imagery and light detection and ranging (LiDAR) data for land cover classification has emerged as a prominent research focus. Despite the satisfactory classification accuracies achieved by existing methodologies, several unaddressed issues that remain warrant consideration. First, current approaches overlook the pronounced spectral and spatial heterogeneities in remote sensing (RS) images designated for multiclassification tasks, limiting the performance of classification models. Moreover, most existing studies amalgamate elevation features with other characteristics through simple addition and interaction operations, and they do not delve deeply into exploiting elevation height information, leading to an imbalance in the representation of elevation height. In light of the aforementioned issues, this article introduces a spatial-spectral heterogeneity-aware network (S2HANet) for the joint classification of HS and LiDAR data. Specifically, a shared spectral correction module (SSCM) is designed in the spectral branch to preliminarily alleviate the problem of large intraclass variance, followed by the use of a contrastive learning framework to enhance the intraclass compactness and interclass separability of spectral features. A multichannel signed distance discrimination module (MCSDDM) is developed to learn the distance relationships between intra- and interclass pixels and boundaries, and using prior boundary information to improve spatial boundary information. In addition, an elevation boost module (EBM) and an elevation injection module (EIM) are meticulously designed to phase-in elevation height information, further enhancing the utilization of elevation data and better facilitating the fusion of the two modalities. The proposed S2HANet has demonstrated exceptional classification performance across three opening benchmark datasets.