A liquid dispenser comprising: a pump housing having a liquid pump chamber and an air pump chamber; a pump plunger in the pump housing, the pump plunger having a center axis that defines mutually perpendicular axial and radial directions and the pump plunger having an interior discharge passage that extends axially through the pump plunger; a liquid piston on the pump plunger and positioned in the liquid pump chamber defining an interior volume of the liquid pump chamber, the liquid piston being moveable between charge and discharge positions in the liquid pump chamber where the liquid piston respectively increases and decreases the Interior volume of the liquid pump chamber; an air piston on the pump plunger and positioned in the air pump chamber defining an interior volume of the air pump chamber, the air piston being moveable between charge and discharge positions in the air pump chamber where the air piston respectively increases and decreases the interior volume of the air pump chamber, and the air piston being moveable with respect to the pump plunger between vent open and vent closed positions of the air piston relative to the pump plunger where in the vent open position of the air piston the air pump chamber is vented to an exterior environment of the dispenser to vent air to the air pump chamber interior volume and in the vent closed position of the air piston the air pump chamber is sealed closed from the exterior environment of the dispenser; a vent hole passing through the air piston; characterised by the pump plunger extending through the air piston vent hole, the air piston vent hole defining a venting air flow path between the plunger and the air piston that vents the air pump chamber interior volume to the exterior environment of the dispenser when the air piston is moved to the vent open position relative to the pump plunger. a pump housing having a liquid pump chamber and an air pump chamber; a pump plunger in the pump housing, the pump plunger having a center axis that defines mutually perpendicular axial and radial directions and the pump plunger having an interior discharge passage that extends axially through the pump plunger; a liquid piston on the pump plunger and positioned in the liquid pump chamber defining an interior volume of the liquid pump chamber, the liquid piston being moveable between charge and discharge positions in the liquid pump chamber where the liquid piston respectively increases and decreases the Interior volume of the liquid pump chamber; an air piston on the pump plunger and positioned in the air pump chamber defining an interior volume of the air pump chamber, the air piston being moveable between charge and discharge positions in the air pump chamber where the air piston respectively increases and decreases the interior volume of the air pump chamber, and the air piston being moveable with respect to the pump plunger between vent open and vent closed positions of the air piston relative to the pump plunger where in the vent open position of the air piston the air pump chamber is vented to an exterior environment of the dispenser to vent air to the air pump chamber interior volume and in the vent closed position of the air piston the air pump chamber is sealed closed from the exterior environment of the dispenser; a vent hole passing through the air piston; characterised by the pump plunger extending through the air piston vent hole, the air piston vent hole defining a venting air flow path between the plunger and the air piston that vents the air pump chamber interior volume to the exterior environment of the dispenser when the air piston is moved to the vent open position relative to the pump plunger.