AbstractIn this paper, we study rare semileptonic decays of the $B_c$ meson in the context of type-I, II, and III two Higgs doublet models. We follow the relativistic quark model for parameterizing the form factors used in matrix elements of weak transitions between the corresponding meson states. We investigate observables such as branching ratio, lepton polarization asymmetry, forward–backward asymmetry, etc. and analyze the dependence of these quantities on the model parameters. We have found that there is noticeable sensitivity to these observables for the charged Higgs boson, which may provide a powerful probe to the standard model and new physics beyond it.