In this work, we study a model of asymmetric two-component lattice fermion system at half-filling, where particles of both species (distinguishable by, e.g., spin) can interact only via nearest-neighbor repulsion W. The analysis is performed on the Bethe lattice using the Hartree-Fock-type mean-field approximation, which is rigorous in the limit of high dimensions. At sufficiently low temperatures, both antiferromagnetic and charge orders (related to inhomogeneous distribution of particles with both spins) coexist in the system. We find that an order-disorder continuous transition occurs with increasing temperature. The transition temperature depends on the ratio t ↑ /t ↓ of the hopping amplitudes of both fermion species (i.e., the asymmetry of the model). For fixed W , it is the biggest if one component is localized (e.g., t ↑ = 0), and it decreases to its minimal value for the same hopping amplitudes (t ↑ = t ↓). Moreover, it increases with W for fixed t ↑ /t ↓. Dependencies of order parameters with model parameters and temperature are also presented. Keywords Order-disorder transition • Two-component fermion model • Intersite repulsion • Mean-field theory • Charge and spin orders • Fermionic gases