In recent years, Humanitarian Organizations (HOs) have been coping with increasing humanitarian needs while faced with budget cuts. It is thus crucial for the HO to efficiently utilize the limited budget in providing humanitarian aids. In this paper, we focus on a HO relief program with a fixed scarce amount of budget to purchase and distribute multitype relief items to beneficiaries with heterogeneous demands. Given the budget, the HO first makes item purchase from external suppliers and then distributes each type of the items equally to the beneficiaries. Equal distribution strategy is a normal practice currently employed in humanitarian operations. However, the strategy fails to tackle demand heterogeneities that inherently exist among beneficiaries, causing significant mismatch between supply and demand. On the other hand, in this study, we point out that the true demand is hardly known by the HO and thus equal distribution can be first taken for fairness concern. To further deal with the mismatch, we borrow the idea from exchange economy and facilitate the HO to set up an item barter channel for beneficiaries. To cope with the demand uncertainty, we employ data-driven analytics taking advantage of the summary statistics about Ukraine refugees during Russo-Ukrainian War and model the demand using moment-based ambiguity set. Consequently, a two-stage distributionally robust optimization (DRO) framework is developed where in the first stage the HO purchases and distributes equally among beneficiaries with a fraction of the fixed budget and in the second stage the HO promotes relief item exchange among refugees with the remaining budget with the goal of minimizing the worse-case expected demand shortage cost. The key decision to make for the HO is to budget allocation for each stage. The DRO model is reformulated into a mixed-integer linear program and solved via cutting plane algorithm efficiently. Numerical experiments show that using a small part of the budget to allow item exchange among refugees could further reduce demand shortage compared to the state-of-the-art approaches.