A paper sheet handling apparatus, comprising: an intake unit through which paper sheets are taken in one by one; a transport unit which transports the paper sheets taken in through the intake unit; a recognition unit which recognizes which of a face or back of each of the paper sheets being transported by the transport unit faces up and how each of the paper sheets being transported by the transport unit is oriented; a stacking unit in which the paper sheets transported by the transport unit are stacked in alignment, with surfaces of an adjacent pair of the paper sheets being in contact with each other; a discharge unit which receives paper sheets that are not accepted by the paper sheet handling apparatus; and a controller which controls transport of the paper sheets to the stacking unit, wherein the controller is configured to: classify the paper sheets into a plurality of types that are different in thickness distribution based on a result of recognition by the recognition unit as to which of the face or back of the paper sheet faces up, and how the paper sheet is oriented; manage the number of paper sheets of each type stacked in the stacking unit; make a determination whether to permit the stacking of the paper sheets in the stacking unit based on the type to which the paper sheets recognized by the recognition unit belong, and the number of paper sheets of each type that have been stacked in the stacking unit; and control the transport unit so that paper sheets which are not permitted to be stacked in the stacking unit are transported to the discharge unit. an intake unit through which paper sheets are taken in one by one; a transport unit which transports the paper sheets taken in through the intake unit; a recognition unit which recognizes which of a face or back of each of the paper sheets being transported by the transport unit faces up and how each of the paper sheets being transported by the transport unit is oriented; a stacking unit in which the paper sheets transported by the transport unit are stacked in alignment, with surfaces of an adjacent pair of the paper sheets being in contact with each other; a discharge unit which receives paper sheets that are not accepted by the paper sheet handling apparatus; and a controller which controls transport of the paper sheets to the stacking unit, wherein the controller is configured to: classify the paper sheets into a plurality of types that are different in thickness distribution based on a result of recognition by the recognition unit as to which of the face or back of the paper sheet faces up, and how the paper sheet is oriented; manage the number of paper sheets of each type stacked in the stacking unit; make a determination whether to permit the stacking of the paper sheets in the stacking unit based on the type to which the paper sheets recognized by the recognition unit belong, and the number of paper sheets of each type that have been stacked in the stacking unit; and control the transport unit so that paper sheets which are not permitted to be stacked in the stacking unit are transported to the discharge unit. classify the paper sheets into a plurality of types that are different in thickness distribution based on a result of recognition by the recognition unit as to which of the face or back of the paper sheet faces up, and how the paper sheet is oriented; manage the number of paper sheets of each type stacked in the stacking unit; make a determination whether to permit the stacking of the paper sheets in the stacking unit based on the type to which the paper sheets recognized by the recognition unit belong, and the number of paper sheets of each type that have been stacked in the stacking unit; and control the transport unit so that paper sheets which are not permitted to be stacked in the stacking unit are transported to the discharge unit.