Network function virtualization enables the “softwarization” of network functions, which are implemented on virtual machines hosted on commercial off-the-shelf servers. Both the composition of the virtual network functions into a forwarding graph (FG) at the logical layer and the embedding of the FG on the servers need to consider the less-than-carrier-grade reliability of COTS components. This letter investigates the tradeoff between end-to-end reliability and computational load per server via the joint design of VNF chain composition (CC) and FG embedding (FGE) under the assumption of a bipartite FG that consists of a controller and regular VNFs. Evaluating the reliability criterion within a probabilistic model, analytical insights are first provided for a simplified disconnected FG. Then, a block coordinate descent method based on mixed-integer linear programming is proposed to tackle the joint optimization of CC and FGE. Via simulation results, it is observed that a joint design of CC and FGE leads to substantial performance gains compared with separate optimization approaches.