We present results of a calculation of the cross section for the production
of a charged Higgs boson in association with an electron and a neutrino at
electron-positron colliders (e+ e- -> H+ e- nu_e-bar, H- e+ nu_e). We study
predictions for the cross section in the Minimal Supersymmetric Standard Model
(MSSM) and the Two Higgs Doublet Model (THDM), highlighting possible
differences. The process is effectively loop-induced in both models. Hence, the
cross section is expected to be strongly model-dependent. Most notably, due to
the presence of superpartners, the MSSM amplitude contains Feynman graphs of
pentagon-type, which are not present in the THDM. This is the first complete
one-loop calculation of the cross section for this process in the THDM and the
MSSM. For both models, so far, only approximate results with limited ranges of
validity were available. Our main aim here is to clarify several open questions
in the existing literature on this process. Specifically, we will discuss the
validity of the Heavy Fermion loop approximation in both models, and of the
Fermion/Sfermion loop approximation in the MSSM.Comment: 21 pages, 8 figures, 1 tabl