Information processing using molecular junctions is becoming more important as devices are miniaturized to the nanoscale. Herein, we report functional molecular junctions derived from double self-assembled monolayers (SAMs) intercalated between soft graphene electrodes. Newly assembled molecular junctions are fabricated by placing a molecular SAM/(top) electrode on another molecular SAM/(bottom) electrode by using a contact-assembly technique. Double SAMs can provide tunneling conjugation across the van der Waals gap between the terminals of each monolayer and exhibit new electrical functions. Robust contact-assembled molecular junctions can act as platforms for the development of equivalent contact molecular junctions between top and bottom electrodes, which can be applied independently to different kinds of molecules to enhance either the structural complexity or the assembly properties of molecules.