The equivalence principle (EP) is one of the basic assumptions of general relativity. Almost all new theories that attempt to unify gravity with the standard model require the EP be broken. Experimental tests of EP provide opportunities for verification of different theoretical models and emergence of new physics. Traditional mass tests[3-9] of EP have achieved the precision of 10-15 level. Tests with quantum properties including spin[10,11], superposition, quantum statistics and internal state[4,13], have been performed, and entanglement test was also proposed. Energy is another very important property and is related to mass by the mass-energy equivalence (MEE). However, mass-energy united tests of EP have never been carried out. Here, we achieve for the first time the united EP test covering energy interval from micro-eV to giga-eV by a mass and internal energy specified atom interferometer (AI). The AI was realized by taking advantage of the Four-Wave Double-diffraction Raman transition (4WDR) method for specified internal energy states, and by extending 4WDR to include excited states. The Eötvös parameters of the four paired combinations (87Rb|F＝1>-85Rb|F＝2>, 87Rb|F＝2>-85Rb|F＝2>, 87Rb|F＝1>-85Rb|F＝3> and 87Rb|F＝2>-85Rb|F＝3>) were measured to be η1=(1.5±3.2)×10-10, η2=(-0.6 ±3.7)×10-10, η3=(-2.5±4.1)×10-10 and η4=(-2.7±3.6)×10-10, respectively. The violation parameters of mass and internal energy are constrained to η0 = (-0.8±1.4)×10-10 and β = (-0.6±6.9)×105. This work opens a door for united tests of EP and MEE in large energy range with quantum systems.