The two human neurotropic alphaherpesviruses varicella-zoster virus (VZV) and herpes simplex virus type 1 (HSV1) both establish latency in sensory ganglia. Human trigeminal ganglia are known to frequently harbor both viruses, and there is evidence to suggest the presence of both VZV and HSV1 DNA in the same neuron. We ask here whether VZV and HSV1 can exclude themselves and each other and whether they can productively infect the same cells in human neurons and human foreskin fibroblasts (HFF). Simultaneous infection (coinfection) or consecutive infection (superinfection) was assessed using cell-free HSV1 and VZV expressing fluorescent reporter proteins. Automated analysis was carried out to detect singly and dually infected cells. We demonstrate that VZV and HSV1 both display efficient superinfection exclusion (SE) in HFF, with each virus excluding either itself or the other virus. While SE also occurred in neurons, it was with much lower efficiency. Both alphaherpesviruses productively infected the same neurons, whether applied simultaneously or even consecutively, albeit at lower frequencies.