Superconducting phonon-cooled hot-electron bolometer (HEB) mixers are promising heterodyne detectors for THz frequencies. KOSMA is working to develop a heterodyne receiver for the GREAT receiver on SOFIA for observation at 1.7-1.9 THz using waveguide mixers. Waveguide mixers at these frequencies require very thin device substrates. We report on recent progress in fabricating and characterizing mixers on 2μm thick silicon nitride membranes which are suspended in a substrate channel. Heterodyne measurements with receiver noise temperatures of 1000K at 800GHz RF and 1GHz IF, at a 4.2K bath temperature show that fabrication of phonon-cooled HEBs on membranes is possible with a good noise performance. The HEB device was fabricated at KOSMA and consists of a 3-5nm thin NbTiN film on an AlN buffer layer.