Multi-material additive manufacturing using thermoplastic extrusion enables the integration of soft and rigid components in a single print operation, yet the interfacial bond strength between new foaming thermoplastic polyurethane (TPU) and engineering-grade filaments remains poorly characterized. This study investigates the bond strength between a foaming TPU filament (Varioshore, colorFabb) and PETG in a lap-joint configuration based on the ASTM 3165 standard, with respect to printing temperature (190 °C, 205 °C, 220 °C, 240 °C) and infill orientation (0° and 45°). Samples were fabricated using a multi-nozzle Prusa XL printer and tested on an MTS hydraulic testing machine. The mean forces recorded were approximately 0.10 kN, 0.21 kN, 0.56 kN, and 0.45 kN at 190°C, 205°C, 220°C, and 240°C, respectively (averaged across both infill orientations), corresponding to bond stresses of 0.6 MPa, 1.3 MPa, 3.5 MPa, and 2.8 MPa. Interestingly, the 220 °C is the optimal printing temperature, yielding the highest bond strength and stiffness, while 240 °C increases elongation-at-break at the cost of bond strength. The 0° infill orientation produced bond up to 50% stronger than the 45° orientation at lower temperatures, with the difference diminishing at higher temperatures. Even under optimal conditions (220°C), the foaming filament bond was approximately 33% weaker than the non-foaming 30D TPU–PETG reference bond, likely due to interface porosity introduced by the foaming agent. The findings are demonstrated through a practical application in the form of a multi-material prosthetic finger design.