The long-standing problem of constructing protein structure alignments is of central importance in computational biology. The main goal is to provide an alignment of residue correspondences, in order to identify homologous residues across chains. A critical next step of this is the alignment of protein complexes and their interfaces. Here, we introduce the program CMAPi, a two-dimensional dynamic programming algorithm that, given a pair of protein complexes, optimally aligns the contact maps of their interfaces: it produces polynomial-time near-optimal alignments in the case of multiple complexes. We demonstrate the efficacy of our algorithm on complexes from PPI families listed in the SCOPPI database and from highly divergent cytokine families. In comparison to existing techniques, CMAPi generates more accurate alignments of interacting residues within families of interacting proteins, especially for sequences with low similarity. While previous methods that use an all-atom based representation of the interface have been successful, CMAPis use of a contact map representation allows it to be more tolerant to conformational changes and thus to align more of the interaction surface. These improved interface alignments should enhance homology modeling and threading methods for predicting PPIs by providing a basis for generating template profiles for sequence-structure alignment.