Material Extrusion (MEX) systems with dual-material capability can unlock interesting applications where flexible and rigid materials are combined. When chemically incompatible materials are concerned the adhesion between the two might be insufficient. Therefore researchers typically rely on dovetail type interlocking geometries in order to affix two bodies mechanically. However, dovetail type interlocking introduces extrusion discontinuities and relies on the material’s resistance to deformation, which is difficult to model. We propose a simple and effective 3D lattice consisting of interlaced horizontal beams in vertically alternating directions which interlock topologically: the interlaced topologically interlocking lattice (ITIL). It ensures continuous extrusion and ensures an interlock even for highly flexible materials. We develop analytical models for optimizing the ultimate tensile strength of the ITIL lattice in two different orientations relative to the interface: straight and diagonal. The analytical models are applied to polypropylene (PP) and polylactic acid (PLA) and verified by finite elements method (FEM) simulations and physical tensile experiments. In the diagonal orientation ITIL can obtain 82% of the theoretical upper bound of 8.6 MPa. ITIL seems to perform comparably to dovetail interlocking designs, while it lends itself to application to non-vertical interfaces. Optimizing the lattice for non-vertical interfaces, however, remains future work.