The iron-based superconductors represent a promising platform for high-temperature superconductivity, but the interactions underpinning their pairing present a puzzle. The EuFe2As2 family is unique among these materials for having magnetic order which onsets within the superconducting state, just below the superconducting transition. Superconductivity and magnetic order are normally antagonistic and often vie for the same unpaired electrons, but in this family the magnetism arises from largely localized Eu moments and they coexist, with the competition between these evenly matched opponents leading to reentrant superconducting behavior. To help elucidate the physics in this family and the interactions between the magnetic order and superconductivity, we investigate the H−T phase diagram near optimal Rh doping through specific heat, resistivity, and magnetization measurements, and study the electronic structure by angular-resolved photoemission spectroscopy. The competition between the Eu and FeAs layers may offer a route to directly access the electronic structure under effective magnetic fields via angle-resolved photoemission spectroscopy, which is ordinarily a strictly zero-field technique.