Holographic-type communication brings an immersive tele-holography experience by delivering holographic contents to users. As the direct representation of holographic contents, hologram videos are naturally three-dimensional representation, which consist of a huge volume of data. Advanced multi-connectivity (MC) millimeter-wave (mmWave) networks are now available to transmit hologram videos by providing the necessary bandwidth. However, the existing link selection schemes in MC-based mmWave networks neglect the source content characteristics of hologram videos and the coordination among the parameters of different protocol layers in each link, leading to sub-optimal streaming performance. To address this issue, we propose a cross-layer-optimized link selection scheme for hologram video streaming over mmWave networks. This scheme optimizes link selection by jointly adjusting the video coding bitrate, the modulation and channel coding schemes (MCS), and link power allocation to minimize the end-to-end hologram distortion while guaranteeing the synchronization and quality balance between real and imaginary components of the hologram. Results show that the proposed scheme can effectively improve the hologram video streaming performance in terms of PSNR by 1.2dB to 6.4dB against the non-cross-layer scheme.