We present an extension to the short-characteristic ray-tracing and non-equilibrium photoionization code C2-Ray. The new version includes the effects of helium and improved multifrequency heating. The motivation for this work is to be able to deal with harder ionizing spectra, such as from quasar-like sources during cosmic reionization. We review the basic algorithmic ingredients of C2-Ray before describing the changes implemented, which include a treatment of the full on-the-spot (OTS) approximation, secondary ionization, and multifrequency photoionization and heating. We performed a series of tests against equilibrium solutions from cloudy as well as comparisons to the hydrogen-only solutions by C2-Ray in the extensive cosmological radiative transfer code comparison project. We show that the full, coupled OTS approximation is more accurate than the simplified, uncoupled one. We find that also with helium and a multifrequency setup, long time-steps (up to ∼ 10 per cent of the recombination time) still give accurate results for the ionization fractions. On the other hand, accurate results for the temperature set strong constraints on the time-step. The details of these constraints depend, however, on the optical depth of the cells. We use the new version of the code to confirm that the assumption made in many reionization simulations, namely that helium is singly ionized everywhere where hydrogen is, is indeed valid when the sources have stellar-like spectra.