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One major concern regarding multi-material additive manufacturing (MMAM) is the strength at the interface between materials. Based on the observation of how nature puts materials together, this paper hypothesizes that overlapping and interlacing materials with each other enhance the interface bonding strength. To test this hypothesis, this research develops a new slicing framework that can efficiently identify the multi-material regions and develop interlaced infills. Based on a ray-tracing technology, we develop layered depth material images (LDMI) to process the material information of digital models for toolpath planning. Each sample point in the LDMI has an associated material and geometric properties that are used to recover the material distribution in each slice. With this material distribution, this work generates an interlocking joint and an interlacing infill in the regions with multiple materials. The experiments include comparisons between similar materials and different materials. Tensile tests have shown that our proposed infill outperforms the interlocking joint in all cases. Fractures occur even outside the interlacing area, meaning that the joint is at least as strong as the materials. The experimental results verify the enhancement of interface strength by overlapping and interlacing materials. In addition, existing computational tools have limitations in full use of material information. To the best of our knowledge, this is the first time a slicer can process overlapped material regions and create interlacing infills. The interlacing infills improve the bonding strength, making the interface no longer the weakest area. This enables MMAM to fabricate truly functional parts. In addition, the new LDMI framework has rich information on geometry and material, and it allows future research in multi-material modeling.