The electric microfield distribution (MFD) at a neutral point is studied for two-component (TCP) electron-ion plasmas using molecular-dynamics simulation and theoretical models. The particles are treated within classical statistical mechanics using an electron-ion Coulomb potential regularized at distances less than the de Broglie length to take into account quantum-diffraction effects. Corrections to the potential-of-mean-force exponential (PMFEX) approximation recently proposed for the MFD at an impurity ion in a strongly coupled TCP [Nersisyan, Phys. Rev. E 72, 036403 (2005)] are obtained and discussed. This has been done by a generalization of the standard Baranger-Mozer and renormalized cluster expansion techniques originally developed for the one-component plasmas to the TCPs. The results from this theoretical model are compared with those from molecular-dynamics simulations. In particular, for a strongly coupled TCP with an ionic charge Z>5 the agreement with numerical simulations is excellent. For still increasing coupling we furthermore found that the PMFEX scheme becomes insufficient to predict the MFD at a neutral point, while its improved version quite well agrees with the simulations.