To Existing research on interdependent networks defines network functions either entirely on nodes or entirely on edges, meaning interdependence between nodes and nodes, or interdependence between edges and edges. However, the reality is not characterized solely by interdependence between individual elements' functionalities, meaning it is not entirely a single-element coupled network. There are cases where both nodes and edges depend on each other. Taking into account this realistic scenario, the paper proposes a binary interdependent network model with coupling between nodes and edges (BINNEC), where both nodes and edges are interdependent. In this model, nodes in network A randomly depend on multiple edges in network B, forming edgedependent clusters. Additionally, a failure tolerance parameter, denoted as μ, is set for these edge-dependent clusters. When the failure rate of an edge-dependent cluster exceeds μ, it results in the failure of the nodes in network A that depend on it. Based on the self-balancing probability method, a theoretical analysis framework is established. Through computer simulation verification of BINNEC under three classical network structures, the model's phase transition behavior and critical thresholds in the face of random attacks are analyzed. The results reveal that BINNEC under three network structures is as fragile as a singleelement coupled network, exhibiting a first-order phase transition behavior. As the size of edge-dependent clusters m increases, network robustness enhances. Moreover, with a constant size of edge-dependent clusters, a larger tolerance for node failure μ leads to stronger network robustness. Finally, the research reveals that under the same conditions of m and μ, when the tolerance for node failure μ is insufficient to withstand the failure of a single edge, the degree distribution widens, and network robustness weakens. However, when the tolerance for node failure is sufficient to withstand the failure of at least one edge, network robustness actually strengthens as the degree distribution increases. These findings provide a theoretical basis for such binary coupled models and also offer guidance for the secure design of real-world networks.