Detecting security vulnerabilities in source code remains challenging, particularly due to class imbalance in real-world datasets where vulnerable functions are under-represented. Existing learning-based methods often optimise for recall, leading to high false positive rates and reduced usability in development workflows. Furthermore, many approaches lack explainability, limiting their integration into security workflows. This paper presents ExplainVulD, a graph-based framework for vulnerability detection in C/C++ code. The method constructs Code Property Graphs and represents nodes using dual-channel embeddings that capture both semantic and structural information. These are processed by an edge-aware attention mechanism that incorporates edge-type embeddings to distinguish among program relations. To address class imbalance, the model is trained using class-weighted cross-entropy loss. ExplainVulD achieves a mean accuracy of 88.25 percent and an F1 score of 48.23 percent across 30 independent runs on the ReVeal dataset. These results represent relative improvements of 4.6 percent in accuracy and 16.9 percent in F1 score compared to the ReVeal model, a prior learning-based method. The framework also outperforms static analysis tools, with relative gains of 14.0 to 14.1 percent in accuracy and 132.2 to 201.2 percent in F1 score. Beyond improved detection performance, ExplainVulD produces explainable outputs by identifying the most influential code regions within each function, supporting transparency and trust in security triage.