Fault tolerance is critical for constructing a reliable service in Network Functions Virtualization (NFV). In this paper, we propose novel models and algorithms that provide the resilience of NFV services from multiple node and link failures. We first design an optimization model and the PAR protection algorithm that can efficiently protect an NFV service demand from network failures without any action from a controller due to the diversity of flow assignment. We then develop an optimization model for total demand protection with a guarantee of recovering the whole demand volume. Further, a new restoration algorithm, namely UNIT, is proposed for the design of large survivable NFV-based networks with the recovery of the affected bandwidth under the uncertainty of multiple network failures. We analytically prove the performance guarantee of UNIT in comparison with the optimal static solution. The results of our experimental study in a Mininet-based environment with the Ryu controller show that a combination of PAR and UNIT efficiently protects NFV-based networks from failures in terms of both resource restoration and recovery time.