Stability of the plane tangential discontinuity (TD) interface in a multi-component dusty plasma (ions, electrons, neutral particles and charged dust) is considered in hydrodynamical approximation. The criterion of stability does not depend on the presence of dust only on one side of the discontinuity but is changed if the dust penetrates through the discontinuity. Therefore, if the instability criterion is marginal, even weak penetration of the dust through the interface may induce Kelvin-Helmholtz instability. This conclusion also refers to cylindrical TD in the presence of dust, so that generation of helical waves in astrophysical jets, type I comet tails, etc. due to the shear driven Kelvin-Helmholtz instability may be hampered in dusty objects of such a geometry.