A Monte Carlo event generator is implemented for a two-Higgs-doublet model with maximal CP symmetry, the MCPM. The model contains five physical Higgs bosons; the  ρ ′, behaving similarly to the standard-model Higgs boson, two extra neutral bosons h ′ and  h ″, and a charged pair  H ± . The special feature of the MCPM is that, concerning the Yukawa couplings, the bosons  h ′, h ″ and H ± couple directly only to the second-generation fermions but with strengths given by the third-generation-fermion masses. Our event generator allows the simulation of the Drell–Yan-type production processes of h ′, h ″ and H ± in proton–proton collisions at LHC energies. Also the subsequent leptonic decays of these bosons into the μ + μ − , μ + ν μ and channels are studied as well as the dominant background processes. We estimate the integrated luminosities needed in pp collisions at center-of-mass energies of 8 and 14 TeV for significant observations of the Higgs bosons h ′, h ″ and H ± in these muonic channels.