Component of the MHF histone-fold complex required for faithful chromosome segregation during meiosis. MHF localizes to centromeres and promotes chromosome segregation (PubMed:24026537). MHF is also the dsDNA-binding component of a FANCM-MHF complex involved in DNA damage repair and genome maintenance. FANCM-MHF promotes gene conversion at blocked replication forks; probably by reversal of the stalled fork (PubMed:20347428; PubMed:24026537). FANCM-MHF promotes non-crossover recombination both in mitotic and meiotic cells (PubMed:22723423; PubMed:24026537). {ECO:0000269|PubMed:20347428; ECO:0000269|PubMed:22723423; ECO:0000269|PubMed:24026537}.