Existing multiple modality fusion methods, such as concatenation, summation, and encoder-decoder-based fusion, have recently been employed to combine modality characteristics of Hyperspectral Image (HSI) and Light Detection And Ranging (LiDAR). However, these methods consider the relationship of HSI-LiDAR signals from limited perspectives. More specifically, they overlook the contextual information across modalities of HSI and LiDAR and the intra-modality characteristics of LiDAR. In this paper, we provide a new insight into feature fusion to explore the relationships across HSI and LiDAR modalities comprehensively. An Interconnected Fusion (IF) framework is proposed. Firstly, the center patch of the HSI input is extracted and replicated to the size of the HSI input. Then, nine different perspectives in the fusion matrix are generated by calculating self-attention and cross-attention among the replicated center patch, HSI input, and corresponding LiDAR input. In this way, the intra- and inter-modality characteristics can be fully exploited, and contextual information is considered in both intra-modality and inter-modality manner. These nine interrelated elements in the fusion matrix can complement each other and eliminate biases, which can generate a multi-modality representation for classification accurately. Extensive experiments have been conducted on three widely used datasets: Trento, MUUFL, and Houston. The IF framework achieves state-of-the-art results on these datasets compared to existing approaches.