A microdosimetric study on nanosecond pulsed electric fields (nsPEF) including cell compartments dispersivity through Debye equation has been detailed in this paper. A quasistatic solution properly adapted for a wide band analysis and coupled with an asymptotic electroporation model has been used to face the problem. Main paper results highlight the relevance of Debye modeling for nsPEF microdosimetry, evidencing that both the trans-membrane potential (TMP) and the pore density are strongly influenced by such a modeling choice. Particularly, an electric (E) field variability up to 70 % has been observed during the pulse rise time, when the high frequency components of the nsPEF prevail, inducing consequently strong pore density alterations within the cell membrane. Furthermore the influence of the use of different membrane dielectric models has been analyzed. The presented results have demonstrated the crucial role of the dielectric membrane characteristics and the importance of their accurate and reliable determination.