The integration of artificial intelligence (AI) with human intelligence (HI) has been asserted to provide transformational power across the humanitarian supply chain (HSC). However, there is little rigorous work that analyses the enablers that promote AI–HI integration and application in the HSC. Thus, this paper reports a hybrid decision support framework for analysing enablers of AI–HI integration in the HSC with complicated, uncertain, and periodic information. First, to collect interdependent preference data from experts, the complex spherical fuzzy weighted Heronian mean operator with a weighted distance measures-based optimization model is established to generate a group decision matrix. Next, to measure the influence strength of enablers, a complex spherical fuzzy decision-making trial and evaluation method is established to determine enabler weights, taking into account their interactive relationships. After that, to explore the enabler level of AI–HI integration in different participants of the HSC, the complex spherical fuzzy measurement of alternatives and ranking according to the compromise solution method is developed by combining the former two procedures. Finally, a case study of enablers analysis for AI–HI integration in HSC is presented to assess the feasibility of the current method, which includes sensitivity and comparison studies. The results reveal that the factor “enhancing the efficiency of relief operations” (0.084) is the most important driving factor for AI–HI integration. The outcomes of this study can provide a new decision support method for understanding the enablers of AI–HI integration in key parts of the HSC.