Stability of open homogeneous flows with shear is a classical subject of fluid mechanics. One of the simplest such flows is a two–dimensional parallel flow of two superimposed immiscible incompressible ideal fluids with constant but non–equal velocities. This flow is unstable for any non–zero velocity difference. Its instability (Kelvin–Helmholtz (KH) instability), however, cannot be used for modelling instabilities of similar flows of two fluids with a sharp velocity variation in a narrow interfacial layer, because the growth rate of the monochromatic waves of the KH instability is a linear function of the wavenumber, implying that an initial–value problem for small localized perturbations in this flow is ill posed. We study unstable wave packets and spatially amplifying waves in a KH–type flow which is like the KH flow with no surface tension, but with one of the fluids being viscous while the other one is inviscid. An initial–value problem for such a flow is well posed, for any value of the velocity jump across the discontinuity. Unstable wave packets are treated analytically and numerically, and the intervals of unstable rays are computed for four representative cases of the density ratio. In reference frames in which the unstable flow is absolutely stable, spatially amplifying waves are analysed. In every such frame, all forcings with non–zero frequencies trigger spatially amplifying waves that amplify in the direction of propagation of convectively unstable wave packets. A possible application of the results to stability of the near flanks of the heliopause is briefly discussed.