[en] We investigate an extension of the Standard Model containing two Higgs doublets and a singlet scalar field (2HDSM). We show that the model can have a strongly first-order phase transition and give rise to the observed baryon asymmetry of the Universe, consistent with all experimental constraints. In particular, the constraints from the electron and neutron electric dipole moments are less constraining here than in pure two-Higgs-doublet model (2HDM). The two-step, first-order transition in 2HDSM, induced by the singlet field, may lead to strong supercooling and low nucleation temperatures in comparison with the critical temperature, T_n≪T_c, which can significantly alter the usual phase-transition pattern in 2HD models with T_n≈T_c. Furthermore, the singlet field can be the dark matter particle. However, in models with a strong first-order transition its abundance is typically but a thousandth of the observed dark matter abundance.