Motivation: Biological molecules perform their functions through interactions with other molecules. Structure alignment of interaction interfaces between biological complexes is an indispensable step in detecting their structural similarities, which are keys to understanding their evolutionary histories and functions. Although various structure alignment methods have been developed to successfully access the similarities of protein structures or certain types of interaction interfaces, existing alignment tools cannot directly align arbitrary types of interfaces formed by protein, DNA or RNA molecules. Specifically, they require a 'blackbox preprocessing' to standardize interface types and chain identifiers. Yet their performance is limited and sometimes unsatisfactory. Results: Here we introduce a novel method, PROSTA-inter, that automatically determines and aligns interaction interfaces between two arbitrary types of complex structures. Our method uses sequentially remote fragments to search for the optimal superimposition. The optimal residue matching problem is then formulated as a maximum weighted bipartite matching problem to detect the optimal sequence order-independent alignment. Benchmark evaluation on all non-redundant protein-DNA complexes in PDB shows significant performance improvement of our method over TM-align and iAlign (with the 'blackbox preprocessing'). Two case studies where our method discovers, for the first time, structural similarities between two pairs of functionally related protein-DNA complexes are presented. We further demonstrate the power of our method on detecting structural similarities between a protein-protein complex and a protein-RNA complex, which is biologically known as a protein-RNA mimicry case. © The Author 2015. Published by Oxford University Press.