Under energy-dissipative cantilevered tip-sample interaction, phase imaging using tapping-mode atomic force microscopy enables compositional mapping of composites containing a harder inorganic phase at the nanometer scale, embedded in a polymer matrix. The contrast in the phase images is shown to be dependent on the variation in the elastic properties of the diblock copolymer reverse micelles loaded with zinc acetate. Tapping conditions are also shown to determine whether the contrast is positive or negative for the harder core of the loaded micelles, based on the competition between attractive and repulsive tip-sample interaction forces. The broader implications are significant for scanning probe microscopy of other soft materials systems containing the segregation of a harder phase.