The interfacial structures, ferroelectric instability, and magnetoelectric coupling effect of FeCo/BaTiO3/FeCo junction with alloy electrode have been studied systematically using the first-principles calculations within density functional theory. Owing to different interfacial coupling between the electrode and BaTiO3 barrier layer, there are four possible interfacial structures, including TiO2/Fe, BaO/Fe, TiO2/Co, and BaO/Co interfaces. Among the four interfacial structures, the TiO2/Fe interface is the most stable one. With the decreasing thickness of BaTiO3 barrier layer in the junction, there exists a critical size of ferroelectricity with a thickness of similar to 4.5 formula unit cells. However, the ferroelectric polarization of magnetoelectric junction with the alloy FeCo electrode is larger than that of the junction with the Co electrode using a same size due to the stronger screening ability of alloy FeCo electrode. Meanwhile, we find that the induced magnetic moments of Ti atoms are nearly from the contribution of the first TiO2 layer adjacent to the interfaces irrespective of the thickness of ferroelectric barrier. In other words, the induced magnetic moments of Ti atoms only maintain an atom-layer thickness. Moreover, the induced magnetic moments of Ti atoms and local magnetic moments of Fe atoms at the two interfaces of tunneling junction depend on the polarization orientation, leading to a sizable ME coupling effect.