Continuous-Time Dynamic Graph (CTDG) methods have shown their superior ability in learning representations for dynamic graph-structured data, the methods split the sequential updating process into discrete batches to reduce the computation costs, as a result, the message constructor in existing CTDG methods cannot be optimized by gradient descent and is designed to be parameter-free. In particular, this layer fails to embed complex event subgraphs and ignores the structure information, while most real-world events are structured and complex. For example, a paper publication event in an academic graph contains different relations like authorship and citations. Furthermore, the corresponding nodes could not receive position-wise messages to make precise representation updates. To tackle this issue, we propose a new method called Temporal Graph Network for continuous-time dynamic Event sequence (TGNE) with a structure-aware message constructor to update node representation with complex event subgraph, by treating message construction and delivery as a message-passing process, in this way, the message constructor can be formalized as a graph neural network layer. TGNE extends the input of CTDG methods to subgraphs with complex structures and preserves more information in message delivery. Extensive experiments demonstrate that the proposed method can achieve competitive performance on traditional tasks on bipartite graphs and event sequence learning tasks on heterogeneous graphs.