Summary: In the real world, directed networks are not just constructed as pairs of directed interactions, but also occur in groups of three or more nodes that form the higher-order structure of the network. From social networks to biological networks, there is growing evidence that real-world systems connect the functional relationships of multiple systems through interdependence. To understand the robustness of interdependent directed higher-order networks, we propose a new theoretical framework to model and analyze the robustness of such networks under random failures by percolation theory. We find that adding higher-order edges makes the network more vulnerable which quantifies and compares by two criteria: the size of the giant connected components and the percolation threshold. Increasing the hyperdegree distribution of heterogeneity or the hyperedge cardinality distribution of heterogeneity in interdependent directed higher-order networks will also make the network more vulnerable. Interestingly, the phase transition type changes from continuous to discontinuous with the increase of coupling strength, and partially interdependent directed higher-order networks exist hybrid phase transition. Moreover, by applying our theoretical analysis to real interdependent directed higher-order networks further validated our conclusion, it has implications for the design of flexible complex systems.