In the face of complex scenarios, the information insufficiency of classification tasks dominated by a single modality has led to a bottleneck in classification performance. The joint application of multimodal remote sensing data for surface observation tasks has garnered widespread attention. However, issues such as sample differences between modalities and the lack of correlation in physical features have limited the performance of classification tasks. Establishing effective interaction between multimodal data has become another significant challenge. To fully integrate heterogeneous information from multiple modalities and enhance classification performance, this paper proposes a dual-branch cross-Transformer feature fusion network aimed at joint land cover classification of hyperspectral imagery (HSI) and Light Detection and Ranging (LiDAR) data. The core idea is to leverage the potential of convolutional operators to represent spatial features, combined with the advantages of the Transformer architecture in learning remote dependencies. The framework employs an improved self-attention mechanism to aggregate features within each modality, highlighting the spectral information of HSI and the spatial (elevation) information of LiDAR. The feature fusion module based on cross-attention integrates deep features from two modalities, achieving complementary information through cross-modal attention. The classification task is performed using jointly obtained spectral and spatial features. Experiments were conducted on three multi-source remote sensing classification datasets, demonstrating the effectiveness of the proposed model compared to existing methods.