Money laundering poses serious threats to financial security, making Anti-Money Laundering (AML) detection crucial. However, the low proportion of money laundering transactions in daily financial activities presents a serious class imbalance challenge for traditional machine learning algorithms. To address this issue and fully exploit graph-structured transaction features, we propose the Wavelet-Enhanced Edge-Attention Multi-Graph Network (WEAMGN), which is designed to learn robust representations that are resilient to class imbalance. Three key components are incorporated in WEAMGN. First, to effectively capture temporal patterns of money laundering activities, we employ adaptive wavelet enhancement to analyze multiscale frequency information over time. Second, recognizing that edges in transaction graphs contain rich information often overlooked by conventional GNNs, WEAMGN introduces an innovative edge information propagation mechanism. In particular, an edge-attention module dynamically assigns weights to multiple edges during node aggregation. This allows the model to emphasize suspicious transactions by assigning them higher attention scores, thereby mitigating the effects of class imbalance. Third, WEAMGN enables the extraction of latent features from both node and edge perspectives. These enriched features are subsequently fed into classifiers for money laundering transaction detection. Experiments on public and real-world AML datasets demonstrate that WEAMGN outperforms existing state-of-the-art methods, confirming its effectiveness and robustness under severe class imbalance.