Automated Essay Scoring (AES) plays a crucial role in educational assessment by providing scalable and consistent evaluations of writing tasks. However, traditional AES systems face three major challenges: (1) reliance on handcrafted features that limit generalizability, (2) difficulty in capturing fine-grained traits like coherence and argumentation, and (3) inability to handle multimodal contexts. In the era of Multimodal Large Language Models (MLLMs), we propose EssayJudge, the first multimodal benchmark to evaluate AES capabilities across lexical-, sentence-, and discourse-level traits. By leveraging MLLMs' strengths in trait-specific scoring and multimodal context understanding, EssayJudge aims to offer precise, context-rich evaluations without manual feature engineering, addressing longstanding AES limitations. Our experiments with 18 representative MLLMs reveal gaps in AES performance compared to human evaluation, particularly in discourse-level traits, highlighting the need for further advancements in MLLM-based AES research.