In this paper, we present a hierarchical method that decomposes a discrete-event system (DES) into a high-level subsystem which communicates with n >= 1 parallel low-level subsystems, through separate interfaces which restrict the interaction of the subsystems. It is a generalization of the serial case (n = 1) described in Part I of this paper, where we define an interface and a set of interface consistency properties that can be used to verify if a DES is nonblocking and controllable. Each clause of the definition can be verified using a single subsystem; thus the complete system model never needs to be stored in memory, offering potentially significant savings in computational resources. We provide algorithms for verifying these new properties, and briefly discuss the computational complexity of the method. Finally, we present an application to a large manufacturing example with an estimated worst-case closed-loop state-space size of 2.9 x 10(21).