Material extrusion-based additive manufacturing (MEX-AM) processes have enabled the fabrication of multi-material structures. Commercially available 3D printers already consist of more than two extruders to print structures with different materials. However, the fabrication of structures with both actuation and sensing (ActSense), in one single process by MEX-AM has been scarcely explored. In this work, we use a multi-material extrusion-based additive manufacturing process to couple magnetic actuation and strain-sensing into one additively manufactured structure. The ActSense multi-functional structure was achieved with a composite based on styrenic block copolymer type thermoplastic elastomer (TPE), soft ferromagnetic and carbon black filler particles. For comparison, elastomeric structures were printed with a composite comprising TPE and soft ferromagnetic filler particles only. In order to achieve improved efficiency, 30 vol% of carbonyl iron particles (CIP) were mixed with the elastomeric matrix. Owing to the fact that CIP and carbon black filler have different densities and a conductive network must be achieved, 15 vol% of each CIP and carbon filler was added to realize the ActSense composites. Morphing membranes with an elastomeric substrate and integrated ActSense elements were analyzed with an additively manufactured custom test setup based on a laser displacement sensor and an electromagnet. With the customized test setup a magnetic field was applied from underneath, and the deformation of the soft structure was analyzed by the laser. Due to the low deformation range, the change in resistance was small, and a diminished piezoresistive behavior of the self-sensing, magnetic composites was obtained. Thereby, to detect the small deformation, a piezoresistive sensing element was extruded separately on top of the magnetoactive part. With this approach, a change in relative resistance at low deformation could be successfully determined. As established by the results, the customized electromagnet-laser sensor setup is an interesting tool for the investigation of soft magnetic materials and structures for shape morphing structures.