Organic-crystal-based optical terahertz (THz) sources and detectors are powerful tools for THz spectroscopy, owing to the wide frequency tunability. A drawback of this technique lies in the inherent absorption peaks of nonlinear crystals, leaving several gaps in the spectral coverage. As an alternative type of organic crystal, hydrogen-bonded OH1 is promising to complement the existing gaps. To demonstrate the potential of OH1, we set up an active and coherent THz frequency-domain system and investigate its performance in difference-frequency generation (DFG) and upconversion (UC) detection. Efficient frequency response extending from 1.58 to 33.38 THz is achieved at room temperature. A strong peak at 31.86 THz is observed for the first time, to the best of our knowledge. Compared with a commercial thermal detector Golay cell, the sensitivity of the OH1-based upconversion detection is 67.8 dB better. These results make it possible to provide a flat and wide THz spectral coverage with a high signal-to-noise ratio by the combination of different types of organic nonlinear crystals.