Among the different fundamental aspects that govern the design and development of elongated multimaterial structures via the preform-to-fiber technique, material association methodologies hold a crucial role. They greatly impact the number, complexity and possible combinations of functions that can be integrated within single fibers, thus defining their applicability. In this work, a co-drawing strategy to produce monofilament microfibers from unique glass-polymer associations is investigated. In particular, the molten core-method (MCM) is applied to several amorphous and semi-crystalline thermoplastics for their integration within larger glass architectures. General conditions in which the MCM can be employed are established. It is demonstrated that the classical glass transition temperature compatibility requirements for glass-polymer associations can be overcome, and that other glass compositions than chalcogenides can be thermally stretched with thermoplastics, here oxide glasses are considered. Composite fibers with various geometries and compositional profiles are then presented to illustrate the versatility of the proposed methodology. Finally, investigations are focused on fibers produced from the association of poly ether ether ketone (PEEK) with tellurite and phosphate glasses. It is demonstrated that upon appropriate elongation conditions, the crystallization kinetics of PEEK can be controlled during the thermal stretching and crystallinities of the polymer as low as 9 mass. % are reached in the final fiber. It is believed such novel material associations as well as the ability to tailor material properties within fibers could inspire the development of a new class of hybrid elongated objects with unprecedented functionalities.