The quantum phase transition, scaling behaviors, and thermodynamics in the spin-1/2 quantum Heisenberg model with antiferromagnetic coupling J > 0 in the armchair direction and ferromagnetic interaction J ′ < 0 in the zigzag direction on a honeycomb lattice are systematically studied using the continuous-time quantum Monte Carlo method. By calculating the Binder ratio Q2 and spin stiffness ρ in two directions for various coupling ratios α = J ′ /J under different lattice sizes, we found that a quantum phase transition from the dimerized phase to the stripe phase occurs at the quantum critical point αc = −0.93. Through the finite-size scaling analysis on Q2, ρx, and ρy, we determined the critical exponent related to the correlation length ν to be 0.7212(8), implying that this transition falls into a classical Heisenberg O(3) universality. A zero magnetization plateau is observed in the dimerized phase, whose width decreases with increasing α. A phase diagram in the coupling ratio α-magnetic field h plane is obtained, where four phases, including dimerized, stripe, canted stripe, and polarized, are identified. It is also unveiled that the temperature dependence of the specific heat C(T ) for different α’s intersects precisely at one point, similar to that of liquid 3He under different pressures and several magnetic compounds under various magnetic fields. The scaling behaviors of Q2, ρ, and C(T ) are carefully analyzed. The susceptibility is compared with the experimental data to give the magnetic parameters of both compounds.