Material extrusion (ME) is an additive manufacturing technique capable of producing functional parts, and its use in multi-material fabrication requires further exploration and expansion. The effectiveness of material bonding is one of the main challenges in multi-material fabrication using ME due to its processing capabilities. Various procedures for improving the adherence of multi-material ME parts have been explored, such as the use of adhesives or the post-processing of parts. In this study, different processing conditions and designs were investigated with the aim of optimizing polylactic acid (PLA) and acrylonitrile–butadiene–styrene (ABS) composite parts without the need for pre- or post-processing procedures. The PLA-ABS composite parts were characterized based on their mechanical properties (bonding modulus, compression modulus, and strength), surface roughness (Ra, Rku, Rsk, and Rz), and normalized shrinkage. All process parameters were statistically significant except for the layer composition parameter in terms of Rsk. The results show that it is possible to create a composite structure with good mechanical properties and acceptable surface roughness values without the need for costly post-processing procedures. Furthermore, the normalized shrinkage and the bonding modulus were correlated, indicating the ability to utilize shrinkage in 3D printing to improve material bonding.