Spatio-temporal stability analysis of a viscosity and density stratified two-fluid flow in a channel with hydrophobic walls, which experience a finite tangential velocity slip, is considered for a range of parameters for which Squire's theorem is not valid. The study restricted only to temporal stability analysis of two/three-dimensional infinitesimal disturbances reveals that three-dimensional disturbances are more unstable than the corresponding two-dimensional disturbances. We examine the role of different types of slip boundary conditions at the channel walls on the temporal growth rate. The influence of velocity slip at the upper wall on the nature of instability in the spatio-temporal framework for low density ratio is investigated, and the boundary that demarcates the convective/absolute instabilities are presented for both two and three-dimensional disturbances. In a configuration with a thinner lower layer away from the upper wall with slip, we found that the flow in the entire domain is absolutely unstable, except for two strips at low and high Reynolds numbers. For the parameters considered in the present study, it is found that the absolutely unstable region shrinks with decrease in velocity slip. The absolute growth rate exhibits a non-monotonic behavior with respect to velocity slip. The role of velocity slip in promoting absolute instability in some parameter regimes suggests that by designing the walls of the channel as hydrophobic/rough/porous surfaces, which can be modelled as smooth surfaces with tangential velocity slip, it may be possible to achieve early transition to turbulence in two-layer flow systems. (C) 2018 Elsevier Ltd. All rights reserved.