Oh. Yes, your response made me think carefully about it and I realized it will be zero. Since the velocity of the liquid, gas and interface is the same that contribution to the momentum bal at the interface will be zero. See figure below for momentum bal at the interface (surface tension effect was neglected). The viscous normal stress term won't cancel out as the liquid and gas viscosities are different. However, the magnitude of this term (eqn in red) is small and won't really affect the physics that much.
To rigorously capture the physics of my problem I will be using the Eulerian model. In my problem, the liquid and gas velocities are different and pressure discontinuity is expected on the interface. For now, i just wanna use VOF to get a quick result and see if the model behaves as expected.