We investigate the full phase diagram of the frustrated J1-J2 Ising model on the two-dimensional honeycomb lattice, incorporating both nearest-neighbor interaction J1 and next-nearest-neighbor interaction J2 using the Wang–Landau Monte Carlo method combined with finite-size scaling analysis. We map out the zero- and finite-temperature phase diagrams as a function of J2/J1. From the entropy profile, we identify four distinct ground-state structures — ferromagnetic, antiferromagnetic, dimer, and stripe states — and confirm that the residual entropy scales linearly with the lattice’s linear dimension in the stripe and dimer ground states. Our results suggest that the transition from the paramagnetic phase into the dimer or stripe phase changes its nature from first-order to continuous while the transition into the ferromagnetic or antiferromagnetic phase is continuous and belongs to the two-dimensional Ising universality class.