Long-range order in the heterogeneous materials architected on various crystal lattices, which have been extensively explored for various engineering functionalities, often culminates in undesirable, intrinsic anisotropy in elasticity and inelasticity in diverse mechanical loading scenarios. In this research, we combine experiments and numerical simulations to design heterogeneous materials that exhibit nearly isotropic elasticity and inelasticity in extreme mechanical deformation events. We design two types of disordered morphologies: dispersed-particle morphology and its interpenetrating counterpart. Representative volume element (RVE) for dispersed-particle morphology is constructed by distributing a finite number of spheres in the unit cube. Then, we generate its interpenetrating counterpart using a simple tessellation via the spatial random points seeded for the dispersed-particle morphology. We then fabricated prototypes for the RVEs of both disordered morphologies using a multi-material 3D printer and conducted large strain mechanical tests on the 3D-printed prototypes under diverse cyclic loading scenarios. Altering the connectivity throughout the disordered network significantly impacted key elastic and inelastic features, including initial stiffness, flow stresses, energy dissipation, and elastic-inelastic shape recovery in the two morphologies upon cyclic loading and unloading conditions. Furthermore, the 3D-printed prototypes with interpenetrating morphology exhibited more robust resilience and energy dissipation performance under repeated loading and unloading cycles. We also examined anisotropy in both morphologies in experiments and numerical simulations. Interestingly, our experiments and numerical simulations disclosed that the interpenetrating morphology exhibited near-complete isotropy in both elasticity and inelasticity with a ``small" number of random spatial points over a range of volume fractions of constituents. Overall, we show that the interpenetrating morphology holds great promise for designing and manufacturing heterogeneous architectures that exhibit isotropic resilience and dissipation under extreme mechanical environments.