With the increasing demands from passengers for data-intensive services, millimeter-wave (mmWave) communication is considered as an effective technique to release the transmission pressure on high speed train (HST) networks. However, mmWave signals ncounter severe losses when passing through the carriage, which decreases the quality of services on board. In this paper, we investigate an intelligent refracting surface (IRS)-assisted HST communication system. Herein, an IRS is deployed on the train window to dynamically reconfigure the propagation environment, and a hybrid time division multiple access-nonorthogonal multiple access scheme is leveraged for interference mitigation. We aim to maximize the overall throughput while taking into account the constraints imposed by base station beamforming, IRS discrete phase shifts and transmit power. To obtain a practical solution, we employ an alternating optimization method and propose a two-stage algorithm. In the first stage, the successive convex approximation method and branch and bound algorithm are leveraged for IRS phase shift design. In the second stage, the Lagrangian multiplier method is utilized for power allocation. Simulation results demonstrate the benefits of IRS adoption and power allocation for throughput improvement in mmWave HST networks.