Birnessites are a variety of hydrous-layered manganese oxides (phyllomanganate) in natural environments and known as the scavenger of heavy metal in nature. Birnessites possess an external and an interlayer surface that are both available for ion adsorption. However, the level of quantitative understanding of metal ion adsorption to birnessite as a function of the environmental conditions is still much smaller than that of metal ion binding to iron and aluminum (hydr)oxides. The main reason for this is that for the latter (hydr)oxides the multi-site surface complexation model including charge distribution (CD-MUSIC) developed by Hiemstra et al. has been worked out in combination with a Stern-Gouy-Chapman (SGC) model of an electrical double layer (EDL), whereas for birnessites only rather simple and not very realistic surface complexation models have been used. In addition, heavy metal adsorption onto birnessite was found to depend on the birnessite microstructure, including the absolute numbers of vacant sites, edge sites and the amount of Mn(III) in the interlayer and in the layer for birnessites with a different Mn average oxidation state (MnAOS). However, some controversy exists on contribution of vacant and edge sites to the total heavy metal adsorption. Therefore, using X-ray diffraction with Rietveld refinement to obtain the reactive sites and their densities, a CD-MUSIC model combined with a Stern-Gouy-Chapman electrical double layer (EDL) model for the external surface and a Donnan model for the interlayer surface is developed for birnessites with different Mn average oxidation state (MnAOS). Proton affinity constants and the charge distributions of Pb surface complexes were calculated a priory. By fitting Pb adsorption data to the model the obtained equilibrium constants (logK_Pb) of Pb complexes were 6.9-10.9 for the double-corner-sharing and double-edge-sharing Pb²⁺ complexes on the edge sites and 2.2-6.5 for the triple-corner-sharing Pb²⁺ complex on the vacancies. The larger logK_Pb value was obtained for higher MnAOS. Speciation calculations showed that with increasing MnAOS from 3.67 to 3.92 the interlayer surface contribution to the total Pb²⁺ adsorption increased from 43.2% to 48.6%, and the vacancy contribution increased from 43.9% to 54.7%. The vacancy contribution from interlayer surface was predominant. The present CD-MUSIC-EDL model contributes to understand better the difference in metal adsorption mechanism between birnessite and iron/aluminum (hydr)oxides and is very useful for improving the accuracy of the risk assessment of heavy metal ion pollution in soils.