Single-phase photoionization equilibrium (PIE) models are often used to infer the underlying physical properties of galaxy halos probed in absorption with ions at different ionization potentials. To incorporate the effects of turbulence, we use the MAIHEM code to model an isotropic turbulent medium exposed to a redshift zero metagalactic UV background, while tracking the ionizations, recombinations, and species-by-species radiative cooling for a wide range of ions. By comparing observations and simulations over a wide range of turbulent velocities, densities, and metallicity with a Markov chain Monte Carlo technique, we find that MAIHEM models provide an equally good fit to the observed low-ionization species compared to PIE models, while reproducing at the same time high-ionization species such as ion{Si}{4} and ion{O}{6}. By including multiple phases, MAIHEM models favor a higher metallicity ($Z/Z_odot approx 40%$) for the circumgalactic medium compared to PIE models. Furthermore, all of the solutions require some amount of turbulence ($sigma_{rm 3D} geqslant 26 {rm km} {rm s}^{-1}$). Correlations between turbulence, metallicity, column density, and impact parameter are discussed alongside mechanisms that drive turbulence within the halo.