In the current article, a defective interface is characterized by "D," representing the smallest diameter of nanosheets crucial for effective conduction transfer from the conductive filler to the medium, and by "ψ" as interfacial conduction. These parameters define the effective aspect ratio and operational volume fraction of graphene in the samples. The resistances of the graphene and polymer layer in contact zones are also considered to determine the contact resistance between adjacent nanosheets. Subsequently, a model for the tunneling conductivity of composites is proposed based on these concepts. This innovative model is validated by experimental data. Additionally, the effects of various factors on the conductivity of the composites and contact resistance are analyzed. Certain parameters such as filler concentration, graphene conductivity, interfacial conduction, and "D" do not affect the contact resistance due to the superconductivity of the nanosheets. However, factors like thin and large nanosheets, short tunneling distance (d), high interfacial conduction (ψ), low "D," and low tunnel resistivity (ρ) contribute to increased conductivity in nanocomposites. The maximum conductivity of 0.09 is obtained at d = 2 nm and ψ = 900 S/m, but d > 6 nm and ψ < 200 S/m produce an insulated sample. Additionally, the highest conductivity of 0.11 S/m is achieved with D = 100 nm and ρ = 100 Ω m, whereas the conductivity approaches 0 at D = 500 nm and ρ = 600 Ω m.