We present the copositivity criteria for the scalar sector of our $S_3 otimes mathbb{Z}_2$ model, which ensures that it is bounded from below. We also show the scalar mass eigenstates, and identify the Standard Model Higgs boson among these by imposing that its Yukawa couplings are the same in our model and the Standard Model. The $Delta rho$ parameter, related to the custodial symmetry, is calculated as well.