Recent progress in Large Language Models (LLMs) has substantially advanced the automation of software engineering (SE) tasks, enabling complex activities such as code generation and code summarization. However, the black-box nature of LLMs remains a major barrier to their adoption in high-stakes and safety-critical domains, where explainability and transparency are vital for trust, accountability, and effective human supervision. Despite increasing interest in explainable AI for software engineering, existing methods lack domain-specific explanations aligned with how practitioners reason about SE artifacts. To address this gap, we introduce FeatureSHAP, the first fully automated, model-agnostic explainability framework tailored to software engineering tasks. Based on Shapley values, FeatureSHAP attributes model outputs to high-level input features through systematic input perturbation and task-specific similarity comparisons, while remaining compatible with both open-source and proprietary LLMs. We evaluate FeatureSHAP on two bi-modal SE tasks: code generation and code summarization. The results show that FeatureSHAP assigns less importance to irrelevant input features and produces explanations with higher fidelity than baseline methods. A practitioner survey involving 37 participants shows that FeatureSHAP helps practitioners better interpret model outputs and make more informed decisions. Collectively, FeatureSHAP represents a meaningful step toward practical explainable AI in software engineering. FeatureSHAP is available at https://github.com/deviserlab/FeatureSHAP.