Mixed micelles containing poly(L-histidine-co-phenylalanine)-poly(ethylene glycol) block copolymer and poly(L-lactic acid)-poly(ethylene glycol) block copolymer are a pH-sensitive drug carrier that release the drug in an acidic microenvironment, but not in the blood. Since the microenvironment of solid tumors is acidic, these mixed micelles are useful for treating cancer, including those cancers exhibiting multidrug resistance. Targeting ligands, such as folate, can also be attached to the mixed micelles for enhancing drug delivery into cells. Methods of treating a warm-blooded animal with such a drug are disclosed.