Phase-separated segmented copolymers comprised of hard and soft segments can be tailored to offer hybrid mechanical performance including a highly dissipative yet resilient large strain behavior. The phase-separated morphology provides multiple relaxation processes which lead to a rate-dependent stress-strain behavior with a transition in rate sensitivity. In addition to the viscoelastic-viscoplastic dissipation pathways, stretch-induced softening due to microstructural breakdown provides a significant source of dissipation as evident in the hysteresis observed during cyclic loading. Extensive shape recovery is observed upon unloading, showing a highly resilient behavior in tandem with extensive dissipation. Here a microstructurally informed three-dimensional constitutive model is developed to capture the remarkable features of the large strain behavior of the segmented copolymers. The model employs multiple micro-rheological mechanisms to capture the time-dependent nonlinear constitutive responses of both hard and soft domains as well as the stretch-induced softening of the hard domains. In direct comparison to experimental data, the model is found to successfully capture the behavior of an exemplar polyurea copolymer over least six orders of magnitude in strain rate (10(-3) to 10(3) s(-1)) including a transition in rate sensitivity at 1 s(-1). The model is also shown to be predictive of the highly dissipative yet resilient stress-strain behavior under a variety of cyclic loading conditions. The microstructurally informed nature of the model provides insights into tailoring copolymeric microstructures to provide tunable energy storage and dissipation mechanisms in this important class of material.