High-energy photon detectors are often made thick in order to improve their photon-detection efficiency. To avoid issues of parallax and increased signal variance that result from random interaction depth, we must determine the 3D interaction position in the imaging detector. With this goal in mind, we examine a method of calibrating response statistics of a thick-detector gamma camera to produce a maximum- likelihood estimate of 3D interaction position. We parameterize the mean detector response as a function of 3D position and estimate the parameters by maximizing their likelihood given prior knowledge of the pathlength distribution and a complete list of camera signals for an ensemble of gamma-ray interactions. Demonstrating this calibration method with simulated gamma-camera data, we show that the resulting calibration is accurate and can be used to produce unbiased estimates of 3D interaction position.