We consider stabilization of nonlinear dynamical systems with hybrid feedback control laws when the communication between the plant and the controller is carried over a digital communication channel, where the information may be subjected to random uncertainties. Adopting the framework of stochastic hybrid systems, we model the randomness in transmissions occurring in the physical communication layer, and the transmission protocols. Stability analysis is carried out for two particular examples: a) Uniting local and global controllers when communicating the discrete variable to the actuator with random dropouts, and b) Event-triggered control algorithms when communicating the state value to the controller where the protocols choose a random time to transmit data after the occurrence of an event.