Tunable multi-chamber microfluidic membrane microlenses with achromaticity over a given focal length range are demonstrated. In analogy to a fixed-focus achromatic doublet lens, the multi-lens system is based on a stack of microfluidic cavities filled with optically optimized liquids with precisely defined refractive index and Abbe number, and these are independently pneumatically actuated. The membranes separating the cavities form the refractive optical surfaces, and the curvatures as a function of pressure are calculated using a mechanical model for deformation of flexible plates. The results are combined with optical ray tracing simulations of the multi-lens system to yield chromatic aberration behavior, which is verified experimentally. A focal length tuning range of 5-40 mm and reduction in chromatic aberration of over 30% is demonstrated, limited by the availability of optical fluids.