Symbiotic binaries are comprised of nebulae, whose densest portions have electron concentrations of 108–1012 cm−3 and extend to a few astronomical units. They are optically thick enough to cause a measurable effect of the scattering of photons on free electrons. In this paper, we model the extended wings of strong emission lines by electron scattering with the aim of determining the electron optical depth, τe, and temperature, Te, of symbiotic nebulae. We have applied our profile-fitting analysis to the broad wings of the O vi 1032, 1038 Å doublet and the He ii 1640 Å emission line, measured in the spectra of symbiotic stars AG Dra, Z And and V1016 Cyg. The synthetic profiles fit the observed wings well. In this way, we have determined τe and Te of the layer of electrons, throughout which the line photons are transferred. During quiescent phases, the mean τe = 0.056 ± 0.006 and Te = 19 200 ± 2300 K, while during active phases, the mean quantities of both parameters increase to τe = 0.64 ± 0.11 and Te = 32 300 ± 2000 K. During quiescent phases, the faint electron-scattering wings are caused mainly by free electrons from/around the accretion disc and the ionized wind from the hot star with the total column density, cm−2. During active phases, the large values of τe are caused by a supplement of free electrons into the binary environment, as a result of the enhanced wind from the hot star, which increases Ne to ∼1024 cm−2.