Clinical notes contain rich patient information, such as diagnoses or medications, making them valuable for patient representation learning. Recent advances in large language models have further improved the ability to extract meaningful representations from clinical texts. However, clinical notes are often missing. For example, in our analysis of the MIMIC-IV dataset, 24.5% of patients have no available discharge summaries. In such cases, representations can be learned from other modalities such as structured data, chest X-rays, or radiology reports. Yet the availability of these modalities is influenced by clinical decision-making and varies across patients, resulting in modality missing-not-at-random (MMNAR) patterns. We propose a causal representation learning framework that leverages observed data and informative missingness in multimodal clinical records. It consists of: (1) an MMNAR-aware modality fusion component that integrates structured data, imaging, and text while conditioning on missingness patterns to capture patient health and clinician-driven assignment; (2) a modality reconstruction component with contrastive learning to ensure semantic sufficiency in representation learning; and (3) a multitask outcome prediction model with a rectifier that corrects for residual bias from specific modality observation patterns. Comprehensive evaluations across MIMIC-IV and eICU show consistent gains over the strongest baselines, achieving up to 13.8% AUC improvement for hospital readmission and 13.1% for ICU admission.