Interest in the magnetic properties of the ordered equiatomic alloy FeRh has been revived in recent years due to potential applications in heat assisted magnetic recording. This is based on the existence of a first order hysteretic phase transition from strongly anisotropic antiferromagnet (AF) to relatively isotropic ferromagnet (F) upon warming to ∼370 K. Here we investigate this transition, which shows significant coupling between structural, magnetic, and electronic degrees of freedom, via wide temperature range magnetotransport and magnetometry measurements on ordered epitaxial MgO(001)/FeRh(1000 Å) films. Consistent with bulk measurements, a large decrease in resistivity (∼30%) occurs on warming through the transition. The transition temperature shifts with applied magnetic field at -0.75 K/kOe due to the field-induced stabilization of the F phase, leading to large negative magnetoresistance (∼40% in 90 kOe) in the transition region (340-400 K). Isothermal field cycles reveal consistent behavior where the resistivity is controlled by the magnetization changes as the AF/F phase boundary is crossed. In the F state at high temperature anisotropic magnetoresistance (AMR) is observed (maximum amplitude ∼0.45%), in addition to high field negative MR due to field-induced suppression of electron-magnon scattering. The temperature dependence of the AMR reveals clear two-phase coexistence in the hysteresis region, providing a sensitive probe of remnant F regions upon cooling through the transition. This behavior, and the accompanying coercivity enhancement, is discussed in terms of possible two-phase microstructures across the magnetic phase transformation.