Deep learning models exhibit state-of-the-art performance for many predictive healthcare tasks using electronic health records (EHR) data, but these models typically require training data volume that exceeds the capacity of most healthcare systems. External resources such as medical ontologies are used to bridge the data volume constraint, but this approach is often not directly applicable or useful because of inconsistencies with terminology. To solve the data insufficiency challenge, we leverage the inherent multilevel structure of EHR data and, in particular, the encoded relationships among medical codes. We propose Multilevel Medical Embedding (MiME) which learns the multilevel embedding of EHR data while jointly performing auxiliary prediction tasks that rely on this inherent EHR structure without the need for external labels. We conducted two prediction tasks, heart failure prediction and sequential disease prediction, where MiME outperformed baseline methods in diverse evaluation settings. In particular, MiME consistently outperformed all baselines when predicting heart failure on datasets of different volumes, especially demonstrating the greatest performance improvement (15% relative gain in PR-AUC over the best baseline) on the smallest dataset, demonstrating its ability to effectively model the multilevel structure of EHR data.