This paper investigates the problem of bi-directional secure information exchange for a multiple-input single-output (MISO) broadcast channel in presence of potential and external eavesdroppers capable of decoding the confidential messages. Specifically, a multi-antenna base station (BS) simultaneously sends wireless information and power to a set of dual-antenna mobile stations (MSs) using power splitters (PSs) in the downlink and receives information in the uplink in full-duplex (FD) mode. We address the joint design of the receiver PS ratio and the transmit power at the MSs, the artificial noise covariance, and the beamforming matrix at the BS in order to guarantee the individual secrecy rate and energy harvesting constraints at each receiver, and the signal-to-interference plus noise ratio (SINR) at the BS and MSs. Using semidefinite relaxation (SDR) technique, we obtain solution to the problem with imperfect channel state information (CSI) of the self-interfering channels. Simulation results are presented to demonstrate the performance of our proposed scheme.