Simultaneous high strength and high toughness are highly sought-after in lattice metamaterials, but these properties are typically mutually exclusive. To overcome this challenge, the development of interpenetrating phase composite (IPC), which incorporates a net matrix infill into the lattice, has shown great potential in overcoming these constraints and is thus of continuous practical interest. In this work, a novel aperiodic monotile truss lattice and polymer IPC that exhibit unprecedented enhancement in both strength and toughness are reported. Specifically, the aperiodic unit cell is inspired by Einstein's monotile, a single space-filling shape where the cell orientation never repeats. The IPCs are achieved through 3D-printed Ti-6Al-4V truss lattices and epoxy infiltration. The highest gain in compressive strength reveals an impressive 246.61% increase, significantly exceeding the “1 + 1 > 2” idealization typically associated with strength in IPC metamaterials. Furthermore, a high specific energy absorption of 46.2 J g−1 demonstrates superior toughness. The underlying mechanisms, including damage sequences, two-phase interactions, and geometric effects between truss and epoxy, are fully elucidated. Overall, this work reports unprecedented enhancement in IPC's properties and demonstrates the potential of utilizing idealized structures to achieve an optimal combination of strength and toughness in mechanical metamaterials.