Using a first-principles approach we investigated an effect of oxygen as substitutional impurity on cohesion of three transition metal nitride multilayers. Namely, we studied AlN/VN, AlN/TiN and VN/TiN systems in a rock-salt structure (B1) with (0 0 1) interfaces. Preferred oxygen positions were determined with the help of calculations of free energy that also included vibrational entropy terms. Subsequent calculations of cleavage energy for all possible cleavage planes enabled us to identify the weakest link and to assess the impact of the oxygen impurity on a cohesion of each of the studied multilayers. Supercells of different size were used to estimate possible effect of oxygen concentration.