We define an interface-interaction network (IIN) to capture the specificity and competition between protein-protein interactions (PPI). This new type of network represents interactions between individual interfaces used in functional protein binding and thereby contains the detail necessary to describe the competition and cooperation between any pair of binding partners. Here we establish a general framework for the construction of IINs that merges computational structure-based interface assignment with careful curation of available literature. To complement limited structural data, the inclusion of biochemical data is critical for achieving the accuracy and completeness necessary to analyze the specificity and competition between the protein interactions. Firstly, this procedure provides a means to clarify the information content of existing data on purported protein interactions and to remove indirect and spurious interactions. Secondly, the IIN we have constructed here for proteins involved in clathrin-mediated endocytosis (CME) exhibits distinctive topological properties. In contrast to PPI networks with their global and relatively dense connectivity, the fragmentation of the IIN into distinctive network modules suggests that different functional pressures act on the evolution of its topology. Large modules in the IIN are formed by interfaces sharing specificity for certain domain types, such as SH3 domains distributed across different proteins. The shared and distinct specificity of an interface is necessary for effective negative and positive design of highly selective binding targets. Lastly, the organization of detailed structural data in a network format allows one to identify pathways of specific binding interactions and thereby predict effects of mutations at specific surfaces on a protein and of specific binding inhibitors, as we explore in several examples. Overall, the endocytosis IIN is remarkably complex and rich in features masked in the coarser PPI, and collects relevant detail of protein association in a readily interpretable format.