This paper investigates the vibration energy transmission between coupled oscillators via their coupling interface, which is characterized by Duffing-type stiffness nonlinearities. Both analytical approximations based on the method of averaging and numerical integrations are employed to obtain the steady-state response and to determine the vibration transmission level. Time-averaged power flow transmission is formulated and used as an index to measure the amount of vibration transmission. It is found that hardening stiffness nonlinearity at the interface can lead to higher vibration power transmission at higher excitation frequencies. In contrast, softening stiffness nonlinearity at the coupling interface can result in higher vibration transmission at lower excitation frequencies. It is also found that the stiffness nonlinearity has a significant effect on vibration transmission in the vicinity of resonant frequency. These findings lead to better understanding of vibration energy transmission mechanisms of nonlinear systems and thus can facilitate enhanced designs of their coupling interfaces for vibration mitigation.