Novel mechanisms for electromagnetic wave emission in the terahertz (THz) frequency regime emerging at the nanometer scale have recently attracted intense attention for the purpose of searching next-generation broadband THz emitters. Here, we report a new mechanism for broadband THz emission, utilizing the interface inverse Rashba-Edelstein effect. By engineering the symmetry of the Ag/Bi Rashba interface, we demonstrate a controllable THz radiation (~0.1-5 THz) waveform emitted from metallic Fe/Ag/Bi heterostructures following photo-excitation. We further reveal that this type of THz radiation can be selectively superimposed on the emission discovered recently due to the inverse Spin Hall effect, yielding a unique film thickness dependent emission pattern. Our results thus offer new opportunities for versatile broadband THz radiation using the interface quantum effects.