Millimeter wave (mmWave) systems are emerging as an essential technology for enabling extremely high data rate wireless communications. The main limiting factors of mmWave systems are blockage (high penetration loss) and deafness (misalignment between the beams of the transmitter and receiver). To alleviate these problems, it is imperative to incorporate efficient association and relaying between terminals and access points. Unfortunately, the existing association techniques are designed for the traditional interference-limited networks, and thus are highly suboptimal for mmWave communications due to narrow-beam operations and the resulting non-negligible interference-free behavior. This paper introduces a distributed approach that solves the joint association and relaying problem in mmWave networks considering the load balancing at access points. The problem is posed as a novel stochastic optimization problem, which is solved by distributed auction algorithms where the clients and relays act asynchronously to achieve optimal client-relay-access point association. It is shown that the algorithms provably converge to a solution that maximizes the aggregate logarithmic utility within a desired bound. Numerical results allow quantification of the performance enhancements introduced by the relays, and the substantial improvements of the network throughput and fairness among the clients by the proposed association method as compared to standard approaches. It is concluded that mmWave communications with proper association and relaying mechanisms can support extremely high data rates, connection reliability, and fairness among the clients.