A jackass-barque, sometimes spelled jackass bark, is a sailing ship with three (or more) masts, of which the foremast is square-rigged and the main is partially square-rigged (topsail, topgallant, etc.) and partially fore-and-aft rigged (course). The mizzen mast is fore-and-aft rigged.
A four-masted jackass barque is square-rigged on the two foremost masts (fore and main masts) and fore-and-aft rigged on the two after masts (the mizzen and spanker or jiggermasts). Some 19th-century sailors called such a ship "a fore-and-aft schooner chasing a brig". In general a jackass barque is a sailing ship which is half square-rigged and half fore-and-aft rigged. The name appears to be an erroneous reference to a mule, which is half horse and half donkey.
A five-masted jackass barque, which has probably never been built, would be equipped with square-rigged fore and main masts, with a partially square-rigged and partially fore-and-aft rigged mizzen mast, and fore-and-aft rigged jigger and spanker masts.