A ray-theoretic phase-space description of linear waves in a two-fluid (charges and neutrals) magnetized plasma is used to calculate analytic decay rates and mode transmission and conversion coefficients between fast and slow waves in two dimensions due to finite ion-neutral collision frequencies at an arbitrary ionization fraction. This is relevant to partially ionized astrophysical plasmas, in particular solar and stellar atmospheres. The most important parameter governing collisional effects is the ratio of the wave frequency to the neutral-charges collision frequency, ϵ = ω/ν nc, with secondary dependence on ionization fraction and wave attack angle. Comparison is made to the one-fluid magnetohydrodynamic case, and it is found that acoustic-to-acoustic and magnetic-to-magnetic transmission through the Alfvén-acoustic equipartition layer is decreased by a term of ${ \mathcal O }({\epsilon }^{2})$ relative to one-fluid (infinite collision frequency), and correspondingly acoustic-to-magnetic and magnetic-to-acoustic conversion is increased. The neutral-acoustic mode is shown to dissipate rapidly as ν nc → ∞. Away from the mode conversion region, dissipative decay along the remaining magneto-acoustic rays scales as ${ \mathcal O }(\epsilon )$ and is found to be much more effective on magnetically dominated rays compared to acoustically dominated rays. This produces a steep jump in dissipation in mode conversion regions, where the rays change character, and can produce localized heating there and beyond. Applications to the solar chromosphere are discussed.