We have constructed a stacked detector system operating in the X-ray range from 0.5 keV to 250 keV that consists of a Si-based 64x64 DePFET-Matrix in front of a CdTe hybrid detector called Caliste-64. The setup is operated under laboratory conditions that approximate the expected environment of a space-borne observatory.The DePFET detector is an active pixel matrix that provides high count-rate capabilities with a near Fanolimited spectral resolution at energies up to 15 keV. The Caliste-64 hard X-ray camera consists of a 1 mm thick CdTe crystal combined with very compact integrated readout electronics, constituting a high performance spectro-imager with event-triggered time-tagging capability in the energy range between 2 keV and 200 keV. In this combined geometry the DePFET detector works as the Low Energy Detector (LED) while the Caliste-64 -as the High Energy Detector (HED) -detects predominantly the high energetic photons that have passed the LED.In addition to the individual optimization of both detectors, we use the setup to test and optimize the performance of the combined detector system. Side-effects like X-ray fluorescence photons, electrical crosstalk, and mutual heating have negative impacts on the data quality and will be investigated. Besides the primary application as a combined imaging detector system with high sensitivity across a broad energy range, additional applications become feasible. Via the analysis of coincident events in both detectors we can estimate the capabilities of the setup to be used as a Compton camera and as an X-ray polarimeter -both desirable functionalities for use in the lab as well as for future X-ray missions.