Terahertz detection with twin superconductor-insulator-superconductor (SIS) tunnel junctions, which are connected in parallel via an inductive thin-film superconducting microstrip line, is mainly studied. Firstly, we investigate the direct-detection response of a superconducting twin-junction device by means of a Fourier transform spectrometer. Secondly, we construct a direct-detection model of twin SIS tunnel junctions. The superconducting twin-junction device is then simulated in terms of the constructed model. The simulation result is found to be in good agreement with the measured one. In addition, we observe that the direct-detection response of the device is consistent with the noise temperature behaviour.