We study the modification of the classical criterion for the linear onset and growing rate of the Kelvin-Helmholtz Instability (KHI) and the Rayleigh-Taylor instability (RTI) in a partially ionised plasma in the two-fluid description. The plasma is composed of a neutral fluid and an electron-ion fluid, coupled by means of particle collisions. The governing linear equations and appropriate boundary conditions, including gravitational terms, are derived and applied to the case a single interface between two partially ionised plasmas. For high collision frequencies and low density contrasts the KHI is present for super-Alfvénic velocity shear only. For high density contrasts the threshold velocity shear can be reduced to sub-Alfvénic values. For the particular case of turbulent plumes in prominences, we conclude that sub-Alfvénic flow velocities can trigger the KHI thanks to the ion-neutral coupling, but with long time scales. Ion-neutral collisions have a strong impact on the RTI growth rate, which can be decreased by an order of magnitude compared to the value in the collisionless case. The time scale for the development of the instability is much longer than in the classical incompressible fully ionised case. This result may explain the existence of prominence fine structures with life times of the order of 30 minutes.