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This paper is devoted to establishing some Hermite–Hadamard-type inequalities for interval-valued functions using the coordinated <i>h</i>-convexity, which is more general than classical convex functions. We also discuss the relationship between coordinated <i>h</i>-convexity and <i>h</i>-convexity. Furthermore, we introduce the concepts of minimum expansion and maximum contraction of interval sequences. Based on these two new concepts, we establish some new Hermite–Hadamard-type inequalities, which generalize some known results in the literature. Additionally, some examples are given to illustrate our results.