It is well known that printing parameters strongly affect the mechanical performance of 3D printed parts. This work explores the role of i) extruder temperature, ii) print speed, and iii) layer height on the interlaminar strength of 3D-printed continuous fibre-reinforced composites. The carbon fibre-reinforced thermoset filament is printed concomitantly with polyethylene terephthalate glycol (PETG) thermoplastic filament in a single nozzle, characterising a continuous fibre co-extrusion (CFC) process. There is a significant variation in the short beam strength for composites printed with different parameters. The load–displacement curves have a similar pattern, with clear load peaks followed by a plastic zone. Optical micrographs and computed tomography (CT) scans reveal that the microstructure is dependent on the printing parameters. Image analysis elucidates the various mechanisms of void formation. Following the application of a three-way ANOVA and statistical tests to quantify the effects and interactions among variables, the analysis concludes that the extruder temperature has the highest influence, followed by print speed and layer height. When considering all possible interactions between the factors, the interaction between print speed and layer height is the most impactful.