Electronic health records (EHRs) are multimodal by nature, consisting of structured tabular features like lab tests and unstructured clinical notes. In real-life clinical practice, doctors use complementary multimodal EHR data sources to get a clearer picture of patients' health and support clinical decision-making. However, most EHR predictive models do not reflect these procedures, as they either focus on a single modality or overlook the inter-modality interactions/redundancy. In this work, we propose MEDFuse, a Multimodal EHR Data Fusion framework that incorporates masked lab-test modeling and large language models (LLMs) to effectively integrate structured and unstructured medical data. MEDFuse leverages multimodal embeddings extracted from two sources: LLMs fine-tuned on free clinical text and masked tabular transformers trained on structured lab test results. We design a disentangled transformer module, optimized by a mutual information loss to 1) decouple modality-specific and modality-shared information and 2) extract useful joint representation from the noise and redundancy present in clinical notes. Through comprehensive validation on the public MIMIC-III dataset and the in-house FEMH dataset, MEDFuse demonstrates great potential in advancing clinical predictions, achieving over 90% F1 score in the 10-disease multi-label classification task.