Deep learning models for clinical event prediction on electronic health records (EHR) often suffer performance degradation when deployed under different data distributions. While domain adaptation (DA) methods can mitigate such shifts, its "black-box" nature prevents widespread adoption in clinical practice where transparency is essential for trust and safety. We propose ExtraCare to decompose patient representations into invariant and covariant components. By supervising these two components and enforcing their orthogonality during training, our model preserves label information while exposing domain-specific variation at the same time for more accurate predictions than most feature alignment models. More importantly, it offers human-understandable explanations by mapping sparse latent dimensions to medical concepts and quantifying their contributions via targeted ablations. ExtraCare is evaluated on two real-world EHR datasets across multiple domain partition settings, demonstrating superior performance along with enhanced transparency, as evidenced by its accurate predictions and explanations from extensive case studies.