In the absence of an initial seed, the Biermann battery term of a non-ideal induction equation acts a source that generates weak magnetic fields. Here, we study this mechanism in the context of partially ionized plasmas, using a model in which the charged and neutral components of the plasma are treated as two different fluids that interact by means of collisions. We investigate the effect that the ionization degree and the charged-neutral interaction have on the generation of magnetic field. We use the numerical code MANCHA-2F to perform 2D simulations of the Kelvin-Helmholtz instability. We study how the magnetic field generated by the Biermann battery process depends on the ionization degree of the plasma and on the different collisional terms included in the equations of the model. We find that when the collisional coupling is taken into account, the generation of magnetic field is increased as the ionization degree is decreased. We also find that this effect depends on the total density of the plasma and that as this parameter is increased, the numerical two-fluid results converge to the analytical results from a single-fluid model.