A fluid supply integration module in a fluid dispensing device includes an on-board reservoir to store fluid, and a fluid interconnect to fluidically couple an external fluid supply container to the on-board reservoir. The fluid supply integration module includes a check valve system disposed between the on-board reservoir and the fluid interconnect. The check valve system includes a first check valve to permit fluid to flow in a first direction and a second check valve to permit air to flow in a second direction opposite the first direction.