Alignment between the injection pipette and the holding pipette/biological entity is crucial for successful cell microinjection. Precision alignment can reduce cell damage and improve cell microinjection. However, in the traditional microscopic vision-based method, lack of depth perception is a drawback in monocular vision. On the other hand, stereo vision with a limited baseline distance and field of view (FOV) makes it challenging to observe biological samples. In this article, a novel hybrid triple-view micro-vision system, in which a binocular telecentric micro-vision unit and an inverted microscope are combined for scene depth and detail sense, is presented for cell microinjection. Based on this system, coarse-to-fine feature extraction methods for two discrepant pipettes are proposed, and a two-stage needle alignment strategy is established based on hybrid pose/image servo control. Some feature extraction and alignment experiments are implemented, and the results demonstrate that the proposed method achieves satisfactory alignment performance (mean position deviation: about 0.1$\mu$m; mean orientation deviation: about 0.4$^\circ$) for zebra embryo microinjection, and the defined symmetry measure can reach 0.09.