The paper studies distributionally robust optimization models with integer recourse. We develop a unified framework that provides finite tight convex relaxations under conic moment-based ambiguity sets and Wasserstein ambiguity sets. They provide tractable primal representations without relying on sampling or semi-infinite optimization. Beyond tractability, the relaxations offer interpretability that captures the criticality of recourse decisions. Finally, it is worth mentioning that our framework applies to distributionally robust chance constraints with integer recourse, which has received limited attention in the literature. The framework is broadly applicable to expectation and conditional value-at-risk measures. In particular, it accommodates distributionally robust chance constraints with integer recourse, which has received limited attention in the literature.