The Internet of Things paradigm enables a new set of smart end-user applications. The Cloud-Fog-Mist-Internet of Things infrastructure provides communication, compute, and storage support for these applications. However, this complex, heterogeneous, and distributed landscape requires orchestration and management mechanisms in order to guarantee their proper functioning. One particular factor to manage is the capacity to provide service resilience even in the presence of failures in components of the substrate infrastructure. This research proposes a set of mechanisms to formalize, orchestrate, and embed a batch of service requests for chained Virtual Functions to fulfill the specific requirements of applications while enhancing their availability and ultimately their resilience. In detail, this work introduces a formal grammar to describe customized Service Chains, allowing the definition of replicas for different Virtual Functions, and an Integer Linear Programming model for Virtual Function embedding that prioritizes the use of nodes with higher availability. Additionally, an alternative heuristic is presented to handle more complex scenarios by taking advantage of the multi-tier scenario comprising the Cloud-Fog-Mist-Internet of Things. Simulation results for the embedding mechanisms show that it is possible to increase the resilience of chained Virtual Functions, while balancing the load of the infrastructure nodes.