The Clouds and the Earth's Radiant Energy System (CERES) is a program that measures the Earth radiation budget (ERB) from two polar orbiting satellite platforms. CERES radiometers are designed to make stable broadband measurements of scattered solar and emitted thermal radiative flux leaving Earth with an accuracy of 1% or better. Using versatile and programmable scan modes, it is also possible for every CERES instrument to view the Moon on each orbit. However, until now, it has not been possible to derive absolute measurements of lunar irradiance using CERES because the Moon's disk fills only 10% of the telescope field of view. This work presents a method of integrating CERES raster-scan data in order to obtain a measurement of the average scattered solar and emitted thermal radiance from the entire lunar disk. The technique results in excellent agreement between CERES instruments on different satellites as to lunar albedo and emitted thermal flux. The average broadband Moon albedo is measured by CERES at a value of 0.1362 (+/-2-3%) when normalized to a static lunar phase angle of 7 degrees using the U.S. Geological Survey lunar irradiance Robotic Lunar Observatory model. The method for the first time also yields very accurate measurements of the thermal irradiance emitted from the Moon. These suggest an average long-wave flux of 977 Wm(-2) (+/-2-3% at 7 degrees phase), implying an approximate mean surface temperature of around 92 degrees C. Statistical analysis on available data suggests that a CERES instrument performing monthly lunar measurements could utilize the Moon as a stability target and reduce calibration drifts to 0.3% per decade or less within an instrument's lifetime. Given the success of the technique, a solar calibration system is proposed that will allow precise tracking of an ERB instrument's optical degradation using the Sun.