The mechanical properties of blends of triblock and diblock copolymers of polystyrene (PS) and polyisoprene (PI) containing 15 wt % PS have been investigated with tensile tests, relaxation tests, dynamic mechanical tests, and hysteresis tests. The properties of binary triblock/diblock blends have been investigated in parallel with those of the same blends diluted with 60 wt % of a low molecular weight but high-T-g solvent, miscible with the PI component but not with the PS domains. Both binary and ternary blends show a nonlinear elastic behavior at large strains, which can be analyzed with rubber elasticity models, and a pronounced nonlinear viscoelastic behavior at intermediate strains. The analysis of the viscoelastic behavior beyond the linear regime shows that the proportion of PI blocks effectively bridging two PS domains controls the deformation of the blends at large strains, while the small and intermediate strain behavior is controlled by the density of entanglements in the rubbery component and by the relaxation of the PI block of the PS-PI diblock. Both of these nonlinear features depend on the diblock/triblock ratio in the blend and will have direct consequences on more complex properties such as fracture or adhesive debonding.