Accurate dispersion management is key for efficient nonlinear light generation. Here, we demonstrate that composite-liquid-core fibers-fibers with binary liquid mixtures as the core medium-allow for accurate and tunable control of dispersion, loss, and nonlinearity. Specifically, we show numerically that mixtures of organic and inorganic solvents in silica capillaries yield anomalous dispersion and reasonable nonlinearity at telecommunication wavelengths. This favorable operation domain is experimentally verified in various liquid systems through dispersion-sensitive supercontinuum generation, with all results being consistent with theoretical designs and simulations. Our results confirm that mixtures introduce a cost-effective means for liquid-core fiber design that allows for loss control, nonlinear response variation, and dispersion engineering.