  We investigate interactions between an elastic membrane and a substrate
characterized by quenched positional disorder in the height function. We show
that the positional disorder transforms the standard secondary DLVO minimum
into two separate states: the hovering state characterized by a planar membrane
at a finite separation from the interface and a pinned state where the membrane
follows closely the asperities of the substrate and is as a consequence quite
corrugated. The transition between the two states is continuous and depends on
the parameters of the underlying DLVO potential as well as the parameters
describing the quenched height-height correlation function of the substrate.
