We have investigated the nonlinear rheology of a soft composite transient network made of a solution of surfactant wormlike micelles (WM) in the semidilute regime that are reversibly bridged by telechelic polymers. The samples are well described, in the linear regime, as two Maxwell fluids components blends, characterized by two markedly different characteristic times. The slow mode is mainly related to the transient network of entangled WM, and the fast mode to the network of telechelic chains. In this paper we investigate the nonlinear viscoelasticity and show that the nonlinear behavior reflects as well the behavior of two coupled networks. On one hand, stress relaxation experiments and time-resolved stress response following the application of a constant shear rate show that, in the weakly nonlinear regime, these novel composite networks stiffen. A fourfold increase of the elastic modulus with respect to the linear value is reached for strain amplitude of about 200%. This strain hardening is due to the nonlinear stretching of the telechelic polymer chains. On the other hand, the samples exhibit shear banding in the highly nonlinear regime, similarly to pure semidilute solutions of WM.