Exemplary embodiments of dispensing systems for dispensing mixtures of multiple liquids, refill units and pumps for such refill units and dispensers are disclosed herein. One refill unit includes a first container and a second container. The refill unit includes a first pump chamber that is associated with the first container and a second pump chamber that is associated with the second container. The first and second pump chambers include a liquid inlet valve and a liquid outlet valve. Expanding the first and second pump chambers draws liquid into the first and second pump chambers through the liquid inlet valves and compressing the first and second pump chambers forces liquid through the liquid outlet valves into a mixing chamber located downstream of the liquid outlet valves. The mixing chamber is formed at least in part by a flexible membrane.; The refill unit also includes an outlet nozzle for dispensing the mixture.