We present an optical system to measure height maps of non-adherent cells as they flow through a microfluidic channel. The cells are suspended in an index-matching absorbing buffer, where cell height is evaluated by measuring the difference in absorption between the cell and the background. Unlike interferometric microscopes, the measured cell height is nearly independent of the cell's optical properties. The height maps are captured using a single exposure of a color camera, and consequently the system is capable of high-throughput characterization of large collections of cells. Using this system, we have measured more than 1600 height maps and volumes of three different leukemia cell lines.