In the real world, the stable operation of a network is usually inseparable from the mutual support of other networks. In such an interdependent network, a node in one layer may depend on multiple nodes in another layer, forming a complex one-to-many dependency relationship. Meanwhile, there may also be higher-order interactions between multiple nodes within a layer, which increases the connectivity within the layer. However, existing research on one-to-many interdependence often neglects intra-layer higher-order structures and lacks a unified theoretical framework for inter-layer dependencies. Moreover, current research on interdependent higher-order networks typically assumes idealized one-to-one inter-layer dependencies, which does not reflect the complexity of real-world systems. These limitations hinder a comprehensive understanding of how such networks withstand failures. Therefore, this paper investigates the robustness of one-to-many interdependent higher-order networks under random attacks. Depending on whether node survival requires at least one dependency edge or multiple dependency edges, we propose four inter-layer interdependency conditions and analyze the network's robustness after cascading failures induced by random attacks. Using percolation theory, we establish a unified theoretical framework that reveals how higher-order interaction structures within intra-layers and inter-layer coupling parameters affect network reliability and system resilience. Additionally, we extend our study to partially interdependent hypergraphs. We validate our theoretical analysis on both synthetic and real-data-based interdependent hypergraphs, offering insights into the optimization of network design for enhanced reliability.