We combine a scanning near-field microwave microscope with an atomic force microscope for use in localized thin film dielectric constant measurement, and demonstrate the capabilities of our system through simultaneous surface topography and microwave reflection measurements on a variety of thin films grown on low resistivity silicon substrates. Reflection measurements clearly discriminate the interface between approximately 38 nm silicon nitride and dioxide thin films at 1.788 GHz. Finite element simulation was used to extract the dielectric constants showing the dielectric sensitivity to be Deltaepsilon(r)=0.1 at epsilon(r)=6.2, for the case of silicon nitride. These results illustrate the capability of our instrument for quantitative dielectric constant measurement at microwave frequencies.