We present a theoretical study of the structure and dynamics of water-carbon tetrachloride liquid-liquid interface by means of ab initio molecular dynamics simulations. We have studied the density profiles, orientational profiles, hydrogen bond distributions, vibrational power spectra, diffusion, orientational relaxation, hydrogen bond dynamics and vibrational spectral diffusion of bulk and interfacial molecules. We have also provided an analysis of vacancies present in the interfacial system using Voronoi polyhedra method. The hydrogen bonding interaction is found to be weakened at the interface compared to that in the bulk phase of water. Weakly hydrogen bonded and non-hydrogen bonded water molecules at the interface give rise to peaks at different positions of the vibrational power spectrum. Diffusion and orientational relaxation of water molecules are also found to be faster at the interface, which can be correlated with the vacancies present in the system. The dynamics of vibrational spectral diffusion is studied by means of frequency-time correlations calculated through a time-series analysis using the wavelet method and the results of spectral diffusion are correlated with the dynamics of hydrogen bond fluctuations and that of non-hydrogen bonded hydroxyl modes in the bulk and interfacial regions.