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The paper presents the results of a theoretical study of the electron- impact ionization of the 6p, 6s, and 5d shells of the Pb and Bi atoms. Calculations are performed using three relativistic approximations, namely distorted waves, Coulomb-Born, and binary-encounter-dipole, in a wide range of collision energies from thresholds to 700 eV. The ionization cross sections of the sub valent 5d shell of the Pb and Bi atoms are calculated for the first time. It is established that this shell contributes to the total direct ionization cross section twice as much as the 6s shell (up to 26% for Pb and up to 38% for Bi), which shows the importance of taking this process into account in modeling different types of plasma. We analyzed the behavior of the partial ionization cross sections of these atoms calculated using various approximations. Comparison of the resultant full direct ionization cross sections with the data of other authors shows that they satisfactorily describe the process of direct ionization. However, for a more detailed analysis and comparison with experimental data additional calculations of the main process of indirect ionization, namely excitation of autoionization, for the Pb and Bi atoms are required. Analysis of the influence of the third valence electron of the Bi atom compared to the Pb atom on the core-valence interaction shows that this influence is the most significant in the case of the distorted waves approximation. The difference in the behavior of the direct ionization cross sections is caused, in our opinion, by the interaction of valence electrons among themselves. [ABSTRACT FROM AUTHOR]