An event-counting method using a two-microchannel plate stack in a low-energy electron point projection microscope is implemented. 15 μm detector spatial resolution, i.e., the distance between first-neighbor microchannels, is demonstrated. This leads to a 7 times better microscope resolution. Compared to previous work with neutrons [Tremsin et al., Nucl. Instrum. Methods Phys. Res., Sect. A 592, 374 (2008)], the large number of detection events achieved with electrons shows that the local response of the detector is mainly governed by the angle between the hexagonal structures of the two microchannel plates. Using this method in point projection microscopy offers the prospect of working with a greater source-object distance (350 nm instead of 50 nm), advancing toward atomic resolution.