Public health emergencies increasingly rely on interconnected artificial intelligence systems to generate epidemiological forecasts, prioritize interventions, allocate scarce resources, and coordinate multi-agency response actions. However, failures during crises rarely originate from a single algorithmic error; they emerge from cumulative governance breakdowns embedded within decision pipelines, including corrupted data lineage, policy-rule divergence, undocumented model updates, fragmented accountability chains, and conflicting interagency directives. These failures often remain invisible until manifested as delayed interventions, inequitable resource distribution, inaccurate risk assessments, or declining public trust. Existing monitoring approaches emphasize model performance and operational metrics but provide limited capability for observing the integrity of decisions as they propagate through complex emergency response ecosystems. This study develops a Decision Integrity Observability Framework (DIOF) that treats decision integrity as a measurable and continuously observable property of AI-enabled public health response networks. The framework introduces integrity telemetry mechanisms that capture governance events across data ingestion, model inference, human override actions, policy enforcement, and cross-organizational coordination layers. A Decision Integrity Deviation Index (DIDI) and Governance Signal Fidelity Score (GSFS) are proposed to quantify the extent to which operational decisions remain aligned with authorized governance intent throughout emergency response cycles. By integrating observability engineering with governance assurance principles, the framework enables early detection of latent governance failures before they cascade into systemic response deficiencies. The resulting architecture establishes a foundation for resilient, auditable, and trustworthy AI-assisted public health emergency management.