In this paper, we show analytically and numerically, that the ultrathin metallic layer up to few monatomic layers separating two ferromagnetic media, which are exchange coupled, can effectively change the phase of the reflected or transmitted spin waves. Taking into account ground states with parallel orientations of the magnetization vectors, we developed the analytical model, which shows the possibility of spin-wave phase control by varying the exchange coupling strength between two ferromagnets. Moreover, we demonstrate with micromagnetic simulations that the effect still exists for the spin waves propagating in thin ferromagnetic film during the reflection or transmission from the interface, where interlayer exchange interactions are present.