<p>Reliability has become a vital performance index of several real-life networks. This study introduces a novel reliability assessment for multistate humanitarian logistics networks (MHLNs), emphasizing their ability to meet all relief demands within pre-determined time constraints and greenhouse gas emissions limit during disaster response. A comprehensive MHLN model is developed, detailing a methodology to identify the minimum paths that remain feasible under time constraints. Reliability is then assessed using minimal path and minimal capacity vector concepts with an efficient recursive sum of disjoint products algorithm. This approach supports realistic, sustainable disaster response planning and provides actionable insights for policymakers. An illustrative case study demonstrates the effectiveness of the algorithm for assessing the reliability of humanitarian logistics operations in disaster and environmental response situations.</p>