A liquid foaming dispenser, comprising: a pump body having an air chamber and a liquid chamber, and defining a central axis that defines mutually perpendicular axial and radial directions; a large piston rod having an air inlet aperture and an air passage, and a hollow interior defining an air-liquid mixing chamber; a large piston positioned at said air chamber and sealingly engaged to said pump body, said large piston being axially movable by said large piston rod; a small piston rod including a small piston base and a liquid passage; a small piston positioned in said liquid chamber and sealingly engaged to said pump body, said small piston being axially movable by said small piston base; and a large piston gasket having a main body portion and a deflection axis passing through said main body portion, said deflection axis being substantially parallel to said central axis, said large piston gasket forming first and second one-way valves, said first one-way valve being formed by a releasable engagement of a first gasket flange against a first sealing surface of said large piston rod, said first gasket flange resiliently and radially outwardly biasing against said first sealing surface at a first location radially outward from said deflection axis, and said second one-way valve being formed by a releasable engagement of a second gasket flange against a second sealing surface of said small piston rod, said second gasket flange resiliently and radially outwardly biasing against said second sealing surface at a second location radially inward from said deflection axis, characterized in that the large piston gasket includes an inlet hole through said body portion; wherein the engagement of said first gasket flange to said first sealing surface is releasable to permit external air to enter said air chamber through said air inlet aperture and said inlet hole, and wherein the engagement of said second gasket flange to said second sealing surface is releasable to permit pressurized air to enter said air-liquid mixing chamber through said air passage. a pump body having an air chamber and a liquid chamber, and defining a central axis that defines mutually perpendicular axial and radial directions; a large piston rod having an air inlet aperture and an air passage, and a hollow interior defining an air-liquid mixing chamber; a large piston positioned at said air chamber and sealingly engaged to said pump body, said large piston being axially movable by said large piston rod; a small piston rod including a small piston base and a liquid passage; a small piston positioned in said liquid chamber and sealingly engaged to said pump body, said small piston being axially movable by said small piston base; and a large piston gasket having a main body portion and a deflection axis passing through said main body portion, said deflection axis being substantially parallel to said central axis, said large piston gasket forming first and second one-way valves, said first one-way valve being formed by a releasable engagement of a first gasket flange against a first sealing surface of said large piston rod, said first gasket flange resiliently and radially outwardly biasing against said first sealing surface at a first location radially outward from said deflection axis, and said second one-way valve being formed by a releasable engagement of a second gasket flange against a second sealing surface of said small piston rod, said second gasket flange resiliently and radially outwardly biasing against said second sealing surface at a second location radially inward from said deflection axis, characterized in that the large piston gasket includes an inlet hole through said body portion; wherein the engagement of said first gasket flange to said first sealing surface is releasable to permit external air to enter said air chamber through said air inlet aperture and said inlet hole, and wherein the engagement of said second gasket flange to said second sealing surface is releasable to permit pressurized air to enter said air-liquid mixing chamber through said air passage.