In this paper, we present a realistic and novel protocol for two-way communication in multiple-input-single-output (MISO) wireless-powered interference channels, namely, a simultaneous wireless information and power transfer (SWIPT) then wireless information transfer (WIT) protocol. In the protocol considered, transmitters first perform SWIPT in a forward link (FL) and receivers and then execute WIT using the harvested energy in a backward link (BL). Given that the operation of SWIPT in the FL affects the performance of WIT in the BL, our aim is to find a resource allocation strategy that maximizes the sum spectral efficiency (SE) of the FL and BL, which requires the joint optimization of the transmit beamforming vector, transmit power, and energy harvesting (EH) ratio in the FL and the receive beamforming vector in the BL. To deal with the non-convexity of the optimization problem, a deep learning (DL) framework is devised, in which the optimal resource allocation strategy is approximated by a well-designed deep neural network (DNN) model consisting of six independent DNN modules where the sigmoid and softmax functions are jointly utilized to properly model each control parameter. Furthermore, a two-stage training method is proposed where the DNN model is initialized using suboptimal solutions that are found using a low complexity algorithm in a supervised manner before it is fine-tuned using the main training based on unsupervised learning. Through intensive simulations performed in various environments, we confirm that the proposed method improves the training performance of the DNN model while reducing the training overhead. As a result, the proposed DL-based resource allocation achieves a near-optimal performance in terms of the sum SE with a low computation time.