Multimaterial additive manufacturing of edible, food-grade soft materials offers a route to spatially organize protein- and lipid-rich domains in structured meat analogues, but it requires rheological compatibility between compositionally distinct inks to maintain stable extrusion, programmable switching, and spatial fidelity. Protein ink and fat-emulsion ink represent a particularly demanding materials pair because they combine a hydrated protein-rich network with an oil-in-water emulsion, resulting in different yielding, recovery, and thermal responses during printing and postprocessing. Here, we introduce rheological synchronization of protein and fat-emulsion inks as a materials design strategy for high-throughput multimaterial three-dimensional (3D) printing of heterogeneous edible soft composites. A xanthan-gum-tuned soy protein ink and a protein-stabilized fat-emulsion ink were formulated to exhibit shear-thinning behavior, synchronized yielding, and rapid post-shear recovery. Microbial transglutaminase-containing formulations further improved structural stability during mild thermal post-curing. When integrated with a parallel Y-junction printing platform, the synchronized inks supported geometrically consistent filament formation across eight nozzles and programmable millimeter-scale switching with limited interfacial blurring. Parallelization increased nominal mass throughput from 0.22 g min−1 in the single-channel configuration to 1.77 g min−1 in the eight-channel configuration, and a 91.2 cm3 whole-cut-inspired heterogeneous construct was fabricated with an active extrusion time of 20 min. The printed edible composites achieved 87.0% fidelity to the digital design and 80.3% protein-domain fidelity to a pork-belly-derived morphological reference, while digitally programmed protein-to-fat-emulsion ratios enabled composition-dependent textural tuning. These results establish rheological synchronization of protein and fat-emulsion inks as a design principle for scalable multimaterial additive manufacturing of structured edible soft materials.