The Alfvén wave is analyzed in case of one quasineutral plasma propagating with some constant speed v0 through another static quasineutral plasma. A dispersion equation is derived describing the Alfvén wave coupled with the flow driven mode ω=kv0 and solutions are discussed analytically and numerically. The usual solutions for two oppositely propagating Alfvén waves are substantially modified due to the flowing plasma. More profound is modification of the solution propagating in the negative direction with respect to the magnetic field and the plasma flow. For a large enough flow speed (exceeding the Alfvén speed in the static plasma), this negative solution may become non-propagating, with frequency equal to zero. In this case it represents a spatial variation of the electromagnetic field. For greater flow speed it becomes a forward mode, and it may merge with the positive one. This merging of the two modes represents the starting point for a flow-driven instability, with two complex-conjugate solutions. The Alfvén wave in interpenetrating plasmas is thus modified and coupled with the flow-driven mode and this coupled mode is shown to be growing when the flow speed is large enough. The energy for the instability is macroscopic kinetic energy of the flowing plasma. The dynamics of plasma particles caused by such a coupled wave still remains similar to the ordinary Alfvén wave. This means that well-known stochastic heating by the Alfvén wave may work, and this should additionally support the potential role of the Alfvén wave in the coronal heating.