Traffic classification is crucial for network management and security. Recently, deep learning-based methods have demonstrated good performance in traffic classification. However, they primarily capture features from raw packet bytes, overlooking the significance of inter-packet correlations within flows from a global perspective. Additionally, effectively handling both packet-length and temporal information, while extracting the structural relationships from a graph into the model, remains a challenge for enhancing the performance of traffic prediction. In this paper, we propose DigTraffic, a novel dual-channel interactive graph transformer to address these limitations. DigTraffic employs a message-level graph-structured flow representation combined with message-aware structural aggregation. To learn intrinsic flow representations, DigTraffic constructs traffic interaction graphs, by incorporating three well-designed heterogeneous types of edges to capture client-server interactions. After that, we separately encode lengthy and temporal flow sequences using a dual-channel network and fuse these modalities within a Transformer architecture. Furthermore, DigTraffic introduces a message-aware Graph Transformer that leverages both node embeddings and edge spatial relations to capture complex graph structures and rich structural information. Experimental results demonstrate that our method significantly outperforms the state-of-the-art methods on four real-world traffic datasets.