Millimeter-wave systems are characterized by the use of highly directional antennas and the presence of blockages, which significantly alter the path-loss and small-scale fading parameters. The received power of each interferer depends on the direction it points and whether it is line-of-sight (LOS), non-LOS (i.e., partially blocked), or completely blocked. While interferers that are sufficiently far away will almost certainly be completely blocked, a finite number of interferers in close proximity will be subject to random partial blockages. Previous attempts to characterize mmWave networks have made the simplifying assumption that all interferers within some radius, called the LOS ball, are unblocked, while interferers beyond that radius are non-LOS. However, compared to simulation results, the LOS ball assumption tends to overestimate outage. In this paper, we present an accurate yet tractable analysis of finite mmWave networks that dispenses with the LOS ball assumption. In the analysis, each interferer has a distribution that is selected randomly from several possibilities, each representing different blockage and directivity states. First, the exact outage probability is found for a finite network with interferers in fixed locations. Then, the spatially averaged outage probability is found by averaging over the interferer locations. While the focus is on device-to-device networks, the analysis is general enough to find applications outside of the present mmWave framework.