A counter-mounted dispenser for dispensing a skincare product includes an above-counter spout and a below-counter drive housing for engaging a replaceable refill unit. The refill unit includes a reservoir configured for holding a volume of skincare fluid, a pump assembly for pumping skincare fluid from the reservoir, and a dispensing tube for delivering the pumped skincare fluid. The reservoir defines a central axis and includes a handle positioned on an outer perimeter of the reservoir. A pump assembly is mounted on the reservoir in a position that is offset from the center of the reservoir in a direction opposite the reservoir's handle.