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Automatic segmentation of vertebral bodies (VBs) and intervertebral discs (IVDs) in 3D magnetic resonance (MR) images is vital in diagnosing and treating spinal diseases. However, segmenting the VBs and IVDs simultaneously is not trivial. Moreover, problems exist, including blurry segmentation caused by anisotropy resolution, high computational cost, inter-class similarity and intra-class variability, and data imbalances. We proposed a two-stage algorithm, named semi-supervised hybrid spine network (SSHSNet), to address these problems by achieving accurate simultaneous VB and IVD segmentation. In the first stage, we constructed a 2D semi-supervised DeepLabv3+ by using cross pseudo supervision to obtain intra-slice features and coarse segmentation. In the second stage, a 3D full-resolution patch-based DeepLabv3+ was built. This model can be used to extract inter-slice information and combine the coarse segmentation and intra-slice features provided from the first stage. Moreover, a cross tri-attention module was applied to compensate for the loss of inter-slice and intra-slice information separately generated from 2D and 3D networks, thereby improving feature representation ability and achieving satisfactory segmentation results. The proposed SSHSNet was validated on a publicly available spine MR image dataset, and remarkable segmentation performance was achieved. Moreover, results show that the proposed method has great potential in dealing with the data imbalance problem. Based on previous reports, few studies have incorporated a semi-supervised learning strategy with a cross attention mechanism for spine segmentation. Therefore, the proposed method may provide a useful tool for spine segmentation and aid clinically in spinal disease diagnoses and treatments. Codes are publicly available at: https://github.com/Meiyan88/SSHSNet.