A fluid model is developed for multicomponent two-temperature magnetized plasmas in chemical non-equilibrium from the partially- to fully-ionized collisional regimes. We focus on transport phenomena aiming at representing the chromosphere of the Sun. Graille et al. [M3AS 19(04):527-599, 2009] have derived an asymptotic fluid model for multicomponent plamas from kinetic theory, yielding a rigorous description of the dissipative effects. The governing equations and consistent transport properties are obtained using a multiscale Chapman-Enskog perturbative solution to the Boltzmann equation based on a non-dimensional analysis. The mass disparity between the electrons and heavy particles is accounted for, as well as the influence of the electromagnetic field. We couple this model to the Maxwell equations for the electromagnetic field and derive the generalized Ohm's law for multicomponent plasmas. The model inherits a well-identified mathematical structure leading to an extended range of validity for the Sun chromosphere conditions. We compute consistent transport properties by means of a spectral Galerkin method using the Laguerre-Sonine polynomial approximation. Two non-vanishing polynomial terms are used when deriving the transport systems for electrons, whereas only one term is retained for heavy particles. In a simplified framework where the plasma is fully ionized, we compare the transport properties for the Sun chromosphere to conventional expressions for magnetized plasmas due to Braginskii, showing a good agreement between both results. For more general partially ionized conditions, representative of the Sun chromosphere, we compute the muticomponent transport properties corresponding to the species diffusion velocities, heavy-particle and electron heat fluxes, and viscous stress tensor of the model, for a Helium-Hydrogen mixture in local thermodynamic equilibrium. The model is assessed for the 3D radiative magnetohydrodynamic simulation of a pore, in the highly turbulent upper layer of the solar convective zone. The resistive term is found to dominate mainly the dynamics of the electric field at the pore location. The battery term for heavy particles appears to be higher at the pore location and at some intergranulation boundaries.