Generative Artificial Intelligence (GenAI) is moving from an experimental productivity tool to an embedded component of managerial analytics, yet organizations still lack a decision architecture that explains when managers should delegate, challenge, verify, or override model outputs. This conceptual study develops a calibrated human–GenAI decision intelligence framework that integrates evidence from management, behavioral decision research, human–automation interaction, explainable artificial intelligence, and responsible artificial intelligence governance. The framework treats decision performance as a joint property of task characteristics, human expertise, model capability, calibration mechanisms, and organizational controls rather than as a property of the model alone. It specifies two coupled layers: a calibration layer that makes uncertainty, evidence quality, and model limitations visible, and a collaboration layer that allocates tasks, preserves human contestability, and creates explicit escalation paths. Eight propositions explain how task ambiguity, decision stakes, expertise, verification friction, explanation quality, and accountability shape appropriate reliance. A six-stage operating loop and a five-level governance maturity model translate the framework into implementable managerial analytics practices. The central implication is that organizations should optimize neither automation nor human control in isolation; they should optimize calibrated complementarity, in which GenAI expands the search and synthesis space while humans retain responsibility for framing, contextual judgment, value-sensitive trade-offs, and final accountability. The framework offers a theory-building platform for empirical research and a practical blueprint for deploying GenAI in managerial decision processes without sacrificing decision quality, organizational learning, or responsible governance.