Most cellular processes are performed by proteomic units that interact with each other. These units are often stoichiometrically stable complexes comprised of several proteins. To obtain a faithful view of the protein interactome we must view it in terms of these basic units (complexes and proteins) and the interactions between them. This study makes two contributions toward this goal. First, it provides a new algorithm for reconstruction of stable complexes from a variety of heterogeneous biological assays; our approach combines state-of-the-art machine learning methods with a novel hierarchical clustering algorithm that allows clusters to overlap. We demonstrate that our approach constructs over 40% more known complexes than other recent methods and that the complexes it produces are more biologically coherent even compared with the reference set. We provide experimental support for some of our novel predictions, identifying both a new complex involved in nutrient starvation and a new component of the eisosome complex. Second, we provide a high accuracy algorithm for the novel problem of predicting transient interactions involving complexes. We show that our complex level network, which we call ComplexNet, provides novel insights regarding the protein-protein interaction network. In particular, we reinterpret the finding that "hubs" in the network are enriched for being essential, showing instead that essential proteins tend to be clustered together in essential complexes and that these essential complexes tend to be large.