The Earth Polychromatic Imaging Camera (EPIC) onboard the Deep Space Climate Observatory (DSCOVR) was designed to measure the atmosphere and surface properties over the whole sunlit half of the Earth from the L1 Lagrangian point. It has 10 spectral channels ranging from the UV to the near-IR, including two pairs of oxygen (O2) A-band (779.5 and 764 nm) and B-band (680 and 687.75 nm) reference and absorption channels selected for the cloud height measurements. This paper presents the radiative transfer analysis pertinent to retrieving cloud top height and cloud geometrical thickness with EPIC A- and B-band observations. Due to photon cloud penetration, retrievals from either O2 A- or B-band channels alone gives the corresponding cloud centroid height, which is lower than the cloud top. However, we show both the sum and the difference between the retrieved cloud centroid heights in the A and B bands are functions of cloud top height and cloud geometrical thickness. Based on this fact, the paper develops a new method to retrieve cloud top height and cloud geometrical thickness simultaneously for fully cloudy scenes over ocean surface. First, cloud centroid heights are calculated for both A and B bands using the ratios between the reflectances of the absorbing and reference channels; then the cloud top height and the cloud geometrical thickness are retrieved from the two dimensional look up tables that relate the sum and the difference between the retrieved centroid heights for A and B bands to the cloud top height and the cloud geometrical thickness. This method is applicable for clouds thicker than an optical depth of 5.