We studied the spin-wave resonance (SWR) frequency and low-temperature magnetization, internal energy, and specific heat of an antiferromagnetic graphene-like bilayer system with two sublattices by applying the retarded Green's function method and the linear spin-wave approximation. The numerical results show that two SWR frequencies in the system can be adjusted by changing the longitudinal magnetic field, interlayer (intralayer) exchange coupling, and intralayer anisotropy. These parameters greatly influence the magnetization, internal energy, and specific heat at low temperatures. Crossovers between the two sublattice magnetizations were observed for the different intralayer exchange couplings, which are affected by the quantum and thermal fluctuations.