Molecular electronics aims to control charge transport at the molecular level, but it is not always clear which factors are important to control because it is difficult to distinguish interface effects from molecular effects. Investigating so-called “odd–even” effects in molecular tunnel junctions provides an opportunity to study molecular effects while keeping the nature of the molecule–electrode interactions unchanged. Odd–even effects in charge tunneling rates have been observed in self-assembled monolayer (SAM)-based tunnel junctions with strong covalent molecule-bottom electrode interactions, but it is not clear whether these odd–even effects originate from the intrinsic properties of the SAM or strong molecule-electrode interactions. Herein, we report tunnel junctions based on SAMs that form on graphene through weak noncovalent interactions (i.e., van der Waals interactions) and also form a van der Waals contact with the top electrode. We found that odd–even effects in charge tunneling rates persist in these junctions with only noncovalent interfaces. AC impedance spectroscopy measurements and molecular dynamics calculations indicate that the odd–even effects of charge transport rates mainly arise from intrinsic properties of the SAM packing, and thus these effects should be considered as a general design rule in future SAM-based junctions.