Purpose Understanding the effect of process parameters on interfaces and interfacial bonding between two materials during multi-material additive manufacturing (MMAM) is crucial to the fabrication of high-quality and strong multi-material structures. The purpose of this paper is to conduct an experimental and statistical study to investigate the effect of process parameters of soft and hard materials on the flexural behavior of multi-material structures fabricated via material extrusion-based MMAM. Design/methodology/approach Sandwich beam samples composed of a soft core and hard shells are fabricated via MMAM under different printing conditions. A design of experiments is conducted to investigate the effect of the print speed and nozzle temperature on the flexural behavior of soft-hard sandwich beams. Analysis of variance and logistic regression analysis are used to analyze the significance of each process parameter. The interfacial morphology of the samples after the flexural tests is characterized. Thermal distributions during the MMAM process are captured to understand the effect of process parameters on the flexural behavior based on inter-bonding formation mechanisms. Findings Experimental results show that the soft-hard sandwich beams exhibited two different failure modes, including shell failure and interfacial failure. A transition of failure modes from interfacial failure to shell failure is observed as the nozzle temperatures increase. The samples that fail because of interfacial cracking exhibit a pure adhesive failure because of weak interfacial fracture properties. The samples that fail because of shell cracking exhibit a mixed adhesive and cohesive failure. The flexural strength and modulus are affected by the nozzle temperature for the hard material and the print speeds for both hard and soft materials significantly. Originality/value This paper first investigates the effect of process parameters for soft and hard materials on the flexural behavior of additively manufactured multi-material structures. Especially, the ranges of the selected process parameters are distinct, and the effect of all possible combinations of the process parameters on the flexural behavior is characterized through a full factorial design of experiments. The experimental results and conclusions of this paper provide guidance for future research on improving the interfacial bonding and understanding the failure mechanism of multi-material structures fabricated by MMAM.