Motivation: 3D visualisation of the spinal cord and vertebrae anatomy is critical for treatment planning and assessment of cord atrophy in neurodegenerative and traumatic diseases. Goal(s): Develop a fully automatic segmentation of the whole spinal cord, vertebrae and discs. Approach: The hybrid method combines a nnU-Net with an iterative processing algorithm with Spinal Cord Toolbox to conveniently generate ground truth labels. We used 3D T1w and T2w scans from three different databases. Results: A validation Dice score of 0.928 was obtained (averaged across contrasts, classes and datasets), suggesting promising segmentation accuracy and capabilities for generalisation given the use of multi-site/multi-vendor datasets. Impact: The fully automatic segmentation of the spine and spinal cord will pinpoint pathologies at specific vertebrae level, offering visualization for surgery preparation. This could also refine segmentation of substructures like multiple sclerosis lesions and tumors, inspiring solutions for related issues.