Liquid-liquid interaction takes place in many applications, such as solvent extraction, oil recovery plants, emulsification, and washing of organic phases. The exchanges can be augmented by container vibrations, which produce instability between the liquids. The present work focuses on the effect of vertical oscillations (parametric sinusoidal forcing) in a liquid-liquid system on the instability threshold and wave amplitude response. The response of two incompressible and immiscible liquids of comparable densities at different depth ratios in a rectangular container subject to parametric sinusoidal forcing, similar to Faraday waves, has been considered. The effect of various depth ratios on the instability threshold and the flow field are investigated for (0, 2) and (0, 4) modes. Numerical simulation has been performed using OpenFOAM to solve Navier-Stokes equations. A source term is added in the interFoam module of OpenFOAM to take the effect of the oscillating container without using any dynamic mesh function. The threshold amplitude and wavenumbers are validated following the linear Floquet analysis of Kumar and Tuckerman (1994). The Floquet analysis showed a substantial shift in natural frequency (reduction) and an increase in threshold amplitude when the interface is in close proximity to the wall. The response amplitude follows a square law with the forcing amplitude for all the depth ratios considered in the present study. The wave amplitude response above the threshold curve shows a logarithmic fit with the liquid depths and forcing parameters.