To maintain the integrity of the genome, multiple DNA repair systems exist to repair damaged DNA. Recognition of altered DNA, including bulky adducts, pyrimidine dimers and interstrand crosslinks (ICL), partially depends on proteins containing helix-hairpin-helix (HhH) domains. To understand how ICL is specifically recognized by the Fanconi anemia proteins FANCM and FAAP24, we determined the structure of the HhH domain of FAAP24. Although it resembles other HhH domains, the FAAP24 domain contains a canonical hairpin motif followed by distorted motif. The HhH domain can bind various DNA substrates; using nuclear magnetic resonance titration experiments, we demonstrate that the canonical HhH motif is required for double-stranded DNA (dsDNA) binding, whereas the unstructured N-terminus can interact with single-stranded DNA. Both DNA binding surfaces are used for binding to ICL-like single/double-strand junction-containing DNA substrates. A structural model for FAAP24 bound to dsDNA has been made based on homology with the translesion polymerase iota. Site-directed mutagenesis, sequence conservation and charge distribution support the dsDNA-binding model. Analogous to other HhH domain-containing proteins, we suggest that multiple FAAP24 regions together contribute to binding to single/double-strand junction, which could contribute to specificity in ICL DNA recognition.