Simultaneous wireless information and power transfer (SWIPT) is a promising communication solution for energy-constrained wireless network. While the interference affects the performance of the system, it also carries energy. In this paper, we investigate an amplify-and-forward (AF) relaying network. In the network, an energy-constrained relay harvests energy from the received RF signal. During the information transmission (IT) period, the relay uses the harvested energy to forward the signal. When the IT is interrupted for some reason, such as strong interference, the relay stores the harvested energy into the energy storage till the interference ends. Particularly, in the IT period, the relay allocates the energy of its storage to the blocks of the IT. Based on the time switching (TS) architecture, the system rates of two energy allocation cases are discussed. It is proved that the scheme based on the energy-allocated-evenly (EAE) is the optimal solution of the system rate maximization, and the mathematical expressions of the system rate based on the EAE scheme is obtained. Then, we discuss the influence of the EAE scheme on the system rate, and the numerical analysis provides practical insights into the effect of two system parameters, namely, interference power and interference factor on the performance of wireless energy harvesting (EH) and IT using AF relay. The results show that the proposed EAE scheme can effectively improve the relaying system rate under an interference channel.