We study the topside ionosphere above the NmF2 ionization maximum and the transition region between the ionosphere and the plasmasphere. We analyze the interaction between the topside ionosphere and the plasmasphere during a strong geomagnetic storm in February 2022, using data from the Irkutsk Incoherent Scatter Radar (IISR) and total electron content data from global navigation satellite systems. To determine the ionosphere and plasmasphere electron contents, an original technique is employed to calculate the integral content of ion density from IISR data, which takes into account the two-component composition of ionospheric plasma. We compare different functions of approximation of the topside ionosphere. The original technique was adjusted for use with IISR Ne data fitted based on the β-Chapman profile. We compare the plasmasphere electron content during quiet and magnetically disturbed days, as well as the dynamics of the O⁺/H⁺ transition height, which is the upper boundary of the ionosphere and the lower boundary of the plasmasphere.