Understanding the electrostatics of a charged semi-permeable plasma membrane is central to quantifying the membrane potential jump and the membrane osmotic pressure that play key roles in a myriad of biological processes ranging from control of intracellular calcium and apoptosis in cancer cells to regulation of cell-antibody or cell-vesicle interactions. In this study, we demonstrate a most remarkable charge inversion (CI) like electrostatics in the cytosol (cell) side of a negatively-charged plasma membrane for the case when the membrane is permeable to a cation and impermeable to an anion. This CI like electrostatics implies a switching of the sign of electrostatic potential from negative to positive from the membrane-cytosol interface to locations deep within the cytosol. Classical electric double layer (EDL) studies have reported such electrostatics manifesting switching of the sign of the electrostatic potential primarily during the occurrence of the CI phenomenon in presence multivalent counterions or ions with finite sizes - here, on the contrary, we witness such an effect on account of the combined influence of the specific sign of the charge and the specific permeability behavior of the cell membrane. We further demonstrate the role of an external permeable salt (both cations and anions of the salt permeate through the membrane) in the membrane electrostatics - presence of the salt invariably lowers the effect of semipermeability by either completely eradicating the CI like electrostatics phenomenon or by substantially reducing the membrane potential jump. Finally, we study the disjoining pressure triggered by the membrane-semipermeability-induced asymmetry in ionic distribution and show the distinct influences of the CI like electrostatics and external salt effects on the disjoining pressure.