Event Argument Extraction (EAE) is the task of identifying roles of entity mentions/arguments in events evoked by trigger words. Most existing works have focused on sentence-level EAE, leaving document-level EAE (i.e., event triggers and arguments belong to different sentences in documents) an under-studied problem in the literature. This paper introduces a new deep learning model for document-level EAE where document structures/graphs are utilized to represent input documents and aid the representation learning. Our model employs different types of interactions between important context words in documents (i.e., syntax, semantic, and discourse) to enhance document representations. Extensive experiments are conducted to demonstrate the effectiveness of the proposed model, leading to the state-of-the-art performance for document-level EAE.