Networks are increasingly used to study the impact of drugs at the systems level. From the algorithmic standpoint, a drug can "attack" nodes or edges of a protein-protein interaction network. In this work, we propose a new network strategy, "The Interface Attack", based on protein-protein interfaces. Similar interface architectures can occur between unrelated proteins. Consequently, in principle, a drug that binds to one has a certain probability of binding to others. The interface attack strategy simultaneously removes from the network all interactions that consist of similar interface motifs. This strategy is inspired by network pharmacology and allows inferring potential off-targets. We introduce a network model that we call "Protein Interface and Interaction Network (P2IN)", which is the integration of protein-protein interface structures and protein interaction networks. This interface-based network organization clarifies which protein pairs have structurally similar interfaces and which proteins may compete to bind the same surface region. We built the P2IN with the p53 signaling network and performed network robustness analysis. We show that (1) "hitting" frequent interfaces (a set of edges distributed around the network) might be as destructive as eleminating high degree proteins (hub nodes), (2) frequent interfaces are not always topologically critical elements in the network, and (3) interface attack may reveal functional changes in the system better than the attack of single proteins. In the off-target detection case study, we found that drugs blocking the interface between CDK6 and CDKN2D may also affect the interaction between CDK4 and CDKN2D.