In this work, we describe a new 3D printing methodology for the fabrication of multimaterial scaffolds involving the combination of thermoplastic extrusion and low temperature extrusion of bioinks. A fiber engraving technique was used to create a groove on the surface of a thermoplastic printed fiber using a commercial 3D printer and a low viscosity bioink was deposited into this groove. In contrast to traditional extrusion bioinks that rely on increased viscosity to prevent lateral spreading, this groove creates a defined space for bioink deposition. By physically constraining bioink spreading, a broader range of viscosities can be used. As proof-of-concept, we fabricated and characterized a multimaterial scaffold containing poly(ε-caprolactone) (PCL) as the thermoplastic polymer and a gelatin-based bioink. A 7.5 w/v% gelatin methacryloyl (GelMA) bioink loaded with either 5 w/v% poly(lactic-co-glycolic acid) (PLGA) microparticles containing fluorescent albumin or mouse fibroblasts (1 × 106 cell/mL) was printed at 24 °C. The structure of the composite scaffolds had no significant decrease in porosity or mechanical properties as compared to the PCL control scaffolds, demonstrating the engraving technique did not significantly compromise the mechanical or structural integrity of the scaffold. The encapsulated PLGA microparticles were homogeneously distributed in the GelMA and remained in the scaffolds after incubation in PBS for 24 h at 37 °C. In addition, the viability of the fibroblasts encapsulated in the GelMA bioink and printed in the grooves of the PCL scaffolds was confirmed after 24 h of incubation. Overall, this work provides a new methodology for the preparation of 3D printed scaffolds containing a robust thermoplastic structure in combination with low viscosity bioinks.