We propose a novel analytical framework for evaluating the coverage performance of a millimeter wave (mmWave) cellular network where idle user equipments (UEs) act as relays. In this network, the base station (BS) adopts either the direct mode to transmit to the destination UE, or the relay mode if the direct mode fails, where the BS transmits to the relay UE and then the relay UE transmits to the destination UE. To address the drastic rotational movements of destination UEs in practice, we propose to adopt selection combining at destination UEs. New expression is derived for the signal-to-interference-plus-noise ratio (SINR) coverage probability of the network. Using numerical results, we first demonstrate the accuracy of our new expression. Then we show that ignoring spatial correlation, which has been commonly adopted in the literature, leads to severe overestimation of the SINR coverage probability. Furthermore, we show that introducing relays into a mmWave cellular network vastly improves the coverage performance. In addition, we show that the optimal BS density maximizing the SINR coverage probability can be determined by using our analysis.