3D-bioprinting is a promising technology applicable in areas such as regenerative medicine or organ model development. Various 3D-bioprinting technologies and systems have been developed and are partly commercially available. Here, we present the construction and characterization of an open-source low-cost 3D-bioprinter that allows the alternated microextrusion of hydrogel and fused deposition modeling (FDM) of thermoplastic filaments. The presented 3D-bioprinter is based on a conventional Prusa i3 MK3 printer and features two independent printheads: the original FDM-head and a syringe-based microextrusion printhead for soft materials. Modifications were designed modularly to fit various syringe formats or heating elements to the device. The bioprinter is the first hybrid DIY 3D-bioprinter that allows switching between materials as often as required during a print run to produce complex multi-material constructs with arbitrary patterns in each layer. For validation of the printer, two designs suitable for relevant bioprinting applications were realized. First, a porous plastic construct filled with hydrogel was printed, serving as a mechanically stable bone replacement tissue model. Second, a plastic chamber, which might be used in organ-on-a-chip applications, was printed with an extruded silicone sealing that enables the liquid-tight attachment of glass slides to the top and bottom of the chamber.