Tissue/organ printing aims to recapitulate the intrinsic complexity of native tissues. For a number of tissues, in particular those of musculoskeletal origin, adequate mechanical characteristics are an important prerequisite for their initial handling and stability, as well as long-lasting functioning. Hence, organized implants, possessing mechanical characteristics similar to the native tissue, may result in improved clinical outcomes of regenerative approaches. Using a bioprinter, grafts were constructed by alternate deposition of thermoplastic fibers and (cell-laden) hydrogels. Constructs of different shapes and sizes were manufactured and mechanical properties, as well as cell viability, were assessed. This approach yields novel organized viable hybrid constructs, which possess favorable mechanical characteristics, within the same range as those of native tissues. Moreover, the approach allows the use of multiple hydrogels and can thus produce constructs containing multiple cell types or bioactive factors. Furthermore, since the hydrogel is supported by the thermoplastic material, a broader range of hydrogel types can be used compared to bioprinting of hydrogels alone. In conclusion, we present an innovative and versatile approach for bioprinting, yielding constructs of which the mechanical stiffness provided by thermoplastic polymers can potentially be tailored, and combined specific cell placement patterns of multiple cell types embedded in a wide range of hydrogels.