Design of highly efficient electromagnetic wave (EMW) absorbing materials with continuous dual-absorption peaks is a hot topic but a challenge in anti-electromagnetic interference and pollution fields. Herein, we developed an interfacial modulation strategy to achieve this goal in dielectric nanocomposite and clarified the interface function and relevant mechanism. Experimentally, CuS/Ag2S composite with tunable heterointerface was fabricated by decorating Ag2S nanoparticles on CuS flakes via cation-exchange reaction. By changing the Ag2S loading, the heterointerface between Ag2S and CuS induced strong dielectric resonant peak and improved impedance matching, which resulted in the significant enhancement of EMW absorption and the appearance of continuous dual-absorption peaks in CuS/Ag2S composite. With a rather low filler loading of 20 wt% and a thin layer thickness of 2.89 mm, the optimized CuS/Ag2S composite exhibited continuous dual-absorption peaks with reflection losses of -47.2 and -20.6 dB, respectively. The proposed interfacial modulation strategy may potentially be used to fabricate other highly efficient dual-absorption absorbers.