A common property of globular clusters (GCs) is to host multiple populations characterized by peculiar chemical abundances. Recent photometric studies suggest that the He content could vary between the populations of a GC by up to ∆He ∼ 0.13, in mass fraction. The initial He content impacts the evolution of low-mass stars by ultimately modifying their lifetimes, luminosity, temperatures, and, more generally, the morphology of post-red giant branch (RGB) evolutionary tracks in the Hertzsprung-Russell diagram. We present new physically accurate isochrones with different initial He enrichments and metallicities, with a focus on the methods implemented to deal with the post-RGB phases. The isochrones are based on tracks computed with the stellar evolution code starevol for different metallicities (Z = 0.0002, 0.0009, 0.002, and 0.008) and with a different He enrichment (from 0.25 to 0.6 in mass fraction). We describe the effect of He enrichment on the morphology of the isochrones, and we tested these by comparing the predicted number counts of horizontal branch and asymptotic giant branch stars with those of selected GCs. Comparing the number ratios, we find that our new theoretical ones agree with the observed values within 1σ in most cases. The work presented here sets the ground for future studies on stellar populations in GCs, in which the abundances of light elements in He-enhanced models will rely on different assumptions for the causes of this enrichment. The developed methodology permits the computation of isochrones from new stellar tracks with noncanonical stellar processes. The checked number counts ensure that, at least in this reference set, the contribution of the luminous late stages of stellar evolution to the integrated light of a GC is represented adequately.