ABSTRACT Supernova (SN) explosions deposit prodigious energy and momentum in their environments, with the former regulating multiphase thermal structure and the latter regulating turbulence and star formation rates in the interstellar medium (ISM). However, systematic studies quantifying the impact of SNe in realistic inhomogeneous ISM conditions have been lacking. Using three-dimensional hydrodynamic simulations, we investigate the dependence of radial momentum injection on both physical conditions (considering a range of mean density n0 = 0.1- ) and numerical parameters. Our inhomogeneous simulations adopt two-phase background states that result from thermal instability in atomic gas. Although the supernova remnant (SNR) morphology becomes highly complex for inhomogeneous backgrounds, the radial momentum injection is remarkably insensitive to environmental details. For our two-phase simulations, the final momentum produced by a single SN is given by . This is only 5% less than the momentum injection for a homogeneous environment with the same mean density, and only 30% greater than the momentum at the time of shell formation. The maximum mass in hot gas is also quite insensitive to environmental inhomogeneity. Strong magnetic fields alter the hot gas mass at very late times, but the momentum injection remains the same. Initial experiments with multiple spatially correlated SNe show a momentum per event nearly as large as single-SN cases. We also present a full numerical parameter study to assess convergence requirements. For convergence in the momentum and other quantities, we find that the numerical resolution Δ and the initial size of the SNR must satisfy , where the shell formation radius is given by for two-phase models (or 30% smaller for a homogeneous medium).