Thickness has been proved to have significant influence on the physical properties of two-dimensional (2D) materials and their corresponding devices. Understanding the effect of the thickness of 2D insertions on the contact properties of metal–monolayer MoS₂ interfaces (viz. metal–mMoS₂ interfaces) is vital to designing high performance mMoS₂ devices. In this work, the electronic structures, Schottky barriers, contact resistance, and tunneling barriers of scandium–mMoS₂ (Sc–mMoS₂) interfaces with BN and graphene insertions have been comparatively studied by density functional theory. No Schottky barriers are found at Sc–mMoS₂ interfaces with monolayer 2D insertions. Although the contact resistance and charge injection efficiency of Sc–mMoS₂ interfaces with monolayer insertions deteriorate relatively to those of the Sc–mMoS₂ interface, they are still sufficient to realize high-performance mMoS₂-based devices. Note that, upon increasing the number of layers of 2D insertions, these contact properties are further deteriorated with the increasing number of layers of insertions. Moreover, additional significant Schottky barriers are introduced into Sc–mMoS₂ interfaces with multilayer BN; the nature Dirac points of graphene insertions are opened, suggesting low performances of Sc–mMoS₂ interfaces with multilayer BN and graphene insertions. These variations can be understood on the basis of the orbital hybridization and charge redistribution between the Sc slab and mMoS₂ layer. In addition, these characteristics are expected to occur in other metal–mMoS₂ interfaces with two-dimensional material insertions. Overall, monolayer rather than multilayer two-dimensional insertions can be used to improve the transport properties of mMoS₂-based devices.