Anti-money laundering (AML) systems are important for protecting the global economy. However, conventional rule-based methods rely on domain knowledge, leading to suboptimal accuracy and a lack of scalability. Graph neural networks (GNNs) for digraphs (directed graphs) can be applied to transaction graphs and capture suspicious transactions or accounts. However, most spectral GNNs do not naturally support multi-dimensional edge features, lack interpretability due to edge modifications, and have limited scalability owing to their spectral nature. Conversely, most spatial methods may not capture the money flow well. Therefore, in this work, we propose LineMVGNN (Line-Graph-Assisted Multi-View Graph Neural Network), a novel spatial method that considers payment and receipt transactions. Specifically, the LineMVGNN model extends a lightweight MVGNN module, which performs two-way message passing between nodes in a transaction graph. Additionally, LineMVGNN incorporates a line graph view of the original transaction graph to enhance the propagation of transaction information. We conduct experiments on two real-world account-based transaction datasets: the Ethereum phishing transaction network dataset and a financial payment transaction dataset from one of our industry partners. The results show that our proposed method outperforms state-of-the-art methods, reflecting the effectiveness of money laundering detection with line-graph-assisted multi-view graph learning. We also discuss scalability, adversarial robustness, and regulatory considerations of our proposed method.