For measuring nanoscale displacements, air/vacuum tunnelling is the most sensitive method. However, the alignment mechanism is difficult to scale down for integrated devices. Here, we present a tunnelling displacement sensor based on a squeezable molecular bilayer, which was built from two stacked self-assembled monolayers of mercaptohexadecanoic acid. The bilayer provides an inherent vertical alignment between the tunnelling electrodes. Squeezing of the bilayer leads to an exponential change in the tunnel current. Nanometre displacement sensitivity was achieved.