We consider stochastic reconnection in a magnetized, partially ionized medium. Stochastic reconnection is a generic effect that results from field line wandering, in which the speed of reconnection is determined by the ability of ejected plasma to diffuse away from the current sheet along magnetic field lines, rather than by the details of current sheet structure. As in earlier work, in which we dealt with a fully ionized plasma, we consider the limit of weak stochasticity, so that the mean magnetic field energy density is greater than either the turbulent kinetic energy density or the energy density associated with the fluctuating component of the field. For specificity, we consider field line stochasticity generated through a turbulent cascade, which leads us to consider the effect of neutral drag on the turbulent cascade of energy. In a collisionless plasma, neutral particle viscosity and ion-neutral drag will damp midscale turbulent motions, but the power spectrum of the magnetic perturbations extends below the viscous cutoff scale. We give a simple physical picture of the magnetic field structure below this cutoff, consistent with numerical experiments. We provide arguments for the reemergence of the turbulent cascade well below the viscous cutoff scale and derive estimates for field line diffusion on all scales. We note that this explains the persistence of a single power-law form for the turbulent power spectrum of the interstellar medium (ISM), from scales of tens of parsecs down to thousands of kilometers. We find that under typical conditions in the ISM stochastic reconnection speeds are reduced by the presence of neutrals, but by no more than an order of magnitude. However, neutral drag implies a steep dependence on the Mach number of the turbulence. In the dense cores of H₂ regions the reconnection speed is probably determined by tearing-mode instabilities.