As plasma membranes of animal cells are known to be asymmetric, the transmembrane lipid asymmetry, being essential for many membranes' properties and functions, should be properly accounted for in model membrane systems. In this paper, we employ atomic-scale molecular dynamics simulations to explore electroporation phenomena in asymmetric model membranes comprised of phosphatidylcholine (PC) and phosphatidylethanolamine (PE) lipid monolayers that mimic the outer and inner leaflets of plasma membranes, respectively. Our findings clearly demonstrate that the molecular mechanism of electroporation in asymmetric phospholipid membranes differs considerably from the picture observed for their single-component symmetric counterparts: The initial stages of electric-field-induced formation of a water-filled pore turn out to be asymmetric and occur mainly on the PC side of the PC/PE membrane. In particular, water molecules penetrate in the membrane interior mostly from the PC side, and the reorientation of lipid head groups, being crucial for stabilizing the hydrophilic pore, also takes place in the PC leaflet. In contrast, the PE lipid head groups do not enter the central region of the membrane until the water pore becomes rather large and partly stabilized by PC head groups. Such behavior implies that the PE leaflet is considerably more robust against an electric field most likely due to interlipid hydrogen bonding. We also show that an electric field induces asymmetric changes in the lateral pressure profile of PC/PE membranes, decreasing the cohesion between lipid molecules predominantly in the PC membrane leaflet. Overall, our simulations provide compelling evidence that the transmembrane lipid asymmetry can be essential for understanding electroporation phenomena in living cells.