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Proton radiography is a widely used experimental method to diagnose the electric and magnetic (EM) fields in high-energy-density plasmas. In proton radiography, the probe protons are typically assumed to be deflected only by the EM fields, whereas the Coulomb scattering caused by the charged particles in the target plasmas is generally ignored. However, at high plasma densities, the presence of Coulomb scattering could reduce the proton flux perturbations recorded on the detector and influence the inversion of the EM fields from experiments. In this paper, a theoretical model is developed for the first time to describe the proton flux distribution on the detector when the EM field deflections and Coulomb scattering coexist in deflecting the probe proton trajectories. Our theory indicates that the Coulomb scattering could decrease the signal contrast of the probed EM fields, which is determined not only by the strengths of the EM field deflections and Coulomb scattering but also by the spatial gradient of the EM fields. Monte Carlo simulations are also conducted to validate our theoretical model. It would be helpful to interpret the proton radiography experiments quantitatively. [ABSTRACT FROM AUTHOR]