<p>As core connecting components in industry, bolts directly determine the operational reliability and safety of equipment via the contact characteristics of their joint interfaces. To tackle the problems of low characterization accuracy and frequent unphysical negative stiffness of traditional asperity contact models under strongly nonlinear loading during bolt tightening, this paper proposes a modified asperity model for bolted joint interfaces based on cubic polynomial interpolation. This model applies unified cubic polynomial interpolation for the coupling relationship among contact load, contact stiffness and contact area with shared boundary conditions, which can effectively ensure continuous and monotonic parameter variation and restrain the occurrence of unphysical negative stiffness in the elastoplastic stage. Firstly, the deformation mechanism of asperities is analyzed, and two rough surfaces are equivalently simplified into a contact model of hemispheroids and rigid planes. Secondly, cubic polynomial interpolation is used to optimize the elastoplastic deformation stage of a single asperity, and formulas for the total contact load and contact stiffness are deduced in combination with Gaussian distribution. Finally, validation is carried out through finite element modal simulation and modal experiments. The results reveal that incorporating joint interfaces enables vibration modes to match actual working conditions better. The average relative error between simulation and test results of the modified model is merely 4.51%, smaller than 8.83% without joint interface contact, 5.74% of the GW model and 4.94% of the Brake model. The model maintains favorable stability and physical consistency under nonlinear loading. Capable of precisely characterizing contact parameters of bolted joint interfaces, this model provides an improved method for research on nonlinear assembly loading and has practical value for health management and precision assembly of high-end equipment.</p>