Meschiidae fam. nov. is erected for the genera Meschia Distant, 1910, containing four species: M. pugnax Distant, 1910 and M. quadrimaculata Distant, 1910 from India, M. woodwardi Scudder, 1957 from Queensland, Australia, and M. barrowensis sp. nov. from Barrow Island, Western Australia, and the related Neomeschia gen. nov. with type species N. queenslandensis sp. nov. from Queensland, Australia. A key to all Australian species and genera is provided. Redescriptions are provided for Meschia, its type species M. pugnax, and M. woodwardi. Relationships, and reasons for the new family placement of Meschia, are discussed.