Intelligent reflect surface (IRS) is a potential technology to build programmable wireless environment in future communication systems. In this paper, we consider an IRS-assisted multi-base station (multi-BS) multi-user millimeter wave (mmWave) downlink communication system, exploiting IRS to extend mmWave signal coverage to blind spots. Considering the impact of IRS on user association in multi-BS mmWave systems, we formulate a sum rate maximization problem by jointly optimizing passive beamforming at IRS, power allocation and user association. This leads to an intractable nonconvex problem, for which to tackle we propose a computationally affordable iterative algorithm, capitalizing on alternating optimization, sequential fractional programming (SFP) and forward-reverse auction (FRA). In particular, passive beamforming at IRS is optimized by utilizing the SFP method, power allocation is solved through means of standard convex optimization method, and user association is handled by the network optimization based FRA algorithm. Simulation results demonstrate that the proposed algorithm can achieve significant performance gains, e.g., it can provide up to 175% higher sum rate compared with the benchmark and 140% higher energy efficiency compared with amplify-and-forward relay.