Quantum optical coherence tomography (QOCT) makes use of an entangled twin-photon light source to carry out axial optical sectioning. We have probed the longitudinal structure of a sample comprising multiple surfaces in a dispersion-cancelled manner while simultaneously measuring the group-velocity dispersion of the interstitial media between the reflecting surfaces. The results of the QOCT experiments are compared with those obtained from conventional optical coherence tomography (OCT).