One of the key challenges in osteochondral tissue engineering is to define specified zones with varying material properties, cell types and biochemical factors supporting locally adjusted differentiation into the osteogenic and chondrogenic lineage, respectively. Herein, extrusion-based core–shell bioprinting is introduced as a potent tool allowing a spatially defined delivery of cell types and differentiation factors TGF-β3 and BMP-2 in separated compartments of hydrogel strands, and, therefore, a local supply of matching factors for chondrocytes and osteoblasts. Ink development was based on blends of alginate and methylcellulose, in combination with varying concentrations of the nanoclay Laponite whose high affinity binding capacity for various molecules was exploited. Release kinetics of model molecules was successfully tuned by Laponite addition. Core–shell bioprinting was proven to generate well-oriented compartments within one strand as monitored by optical coherence tomography in a non-invasive manner. Chondrocytes and osteoblasts were applied each in the shell while the respective differentiation factors (TGF-β3, BMP-2) were provided by a Laponite-supported core serving as central factor depot within the strand, allowing directed differentiation of cells in close contact to the core. Experiments with bi-zonal constructs, comprising an osteogenic and a chondrogenic zone, revealed that the local delivery of the factors from the core reduces effects of these factors on the cells in the other scaffold zone. These observations prove the general suitability of the suggested system for co-differentiation of different cell types within a zonal construct.