We study the two-stage inventory fulfillment problem with multiple upstream suppliers and multiple downstream retailers in the real world with uncertain demand and uncertain supply. The central decision maker determines the production quantities of suppliers before knowing the actual demand and available supply and the allocation quantities after the randomness is realized. We take a target-based distributional robust optimization approach with a moment-based ambiguity set, which formulates the moment distribution information of uncertainties and the correlation among them. Moreover, we propose a new decision criterion ”Weighted-Fairness Robust Risk Index (WFRI)” that considers the fairness of the allocation results and uniform risk measure of target violation as our objective. Also, we show the advantages of our model over the individual models, where the retailers make ordering decisions for the upstream suppliers by themselves. For computational tractability, we adopt the quadratic decision rule method to approximate the adaptive decisions, by which we finally get a solvable SDP optimization problem. In the numerical study, we have shown the good performance of our DRO WFRI method compared with the other three benchmarks and analyzed the pooling effect, scenario values, and the superiority of our uniform and fair risk measures to achieve targets and attain the fairest allocation. The robustness of our method has also been verified.