We present adaptive mesh refinement (AMR) hydrodynamical simulations of the interaction between Type Ia supernovae and their companion stars within the context of the single-degenerate model. Results for 3D red-giant companions without binary evolution agree with previous 2D results by Marietta et al. We also consider evolved helium-star companions in 2D. For a range of helium-star masses and initial binary separations, we examine the mass unbound by the interaction and the kick velocity delivered to the companion star. We find that unbound mass versus separation obeys a power law with index between -3.1 and -4.0, consistent with previous results for hydrogen-rich companions. Kick velocity also obeys a power-law relationship with binary separation, but the slope differs from those found for hydrogen-rich companions. Assuming accretion via Roche-lobe overflow, we find that the unbound helium mass is consistent with observational limits. Ablation (shock heating) appears to be more important in removing gas from helium-star companions than from hydrogen-rich ones, though stripping (momentum transfer) dominates in both cases.