We present a comprehensive experimental and theoretical study of the electronic and magnetic properties of two quasi-two-dimensional (2D) honeycomb lattice monoclinic compounds A3Ni2SbO6(A=Li,Na). Magnetic susceptibility and specific heat data are consistent with the onset of antiferromagnetic long-range order with Néel temperatures of ∼14 and 16 K for Li3Ni2SbO6 and Na3Ni2SbO6, respectively. The effective magnetic moments of 4.3μB/f.u.(Li3Ni2SbO6) and 4.4μB/f.u.(Na3Ni2SbO6), where f.u. is formula units, indicate that Ni2+ is in a high-spin configuration (S=1). The temperature dependence of the inverse magnetic susceptibility follows the Curie-Weiss law in the high-temperature region and shows positive values of the Weiss temperature, ∼8K (Li3Ni2SbO6) and ∼12 K (Na3Ni2SbO6), pointing to the presence of nonnegligible ferromagnetic interactions, although the system orders antiferromagnetically at low temperatures. In addition, the magnetization curves reveal a field-induced (spin-flop type) transition below TN that can be related to the magnetocrystalline anisotropy in these systems. These observations are in agreement with density functional theory calculations, which show that both antiferromagnetic and ferromagnetic intralayer spin exchange couplings between Ni2+ ions are present in the honeycomb planes, supporting a zigzag antiferromagnetic ground state. Based on our experimental measurements and theoretical calculations, we propose magnetic phase diagrams for the two compounds.