Integrating large intelligent reflecting surfaces (IRS) into millimeter-wave (mmWave) massive multi-input-multi-ouput (MIMO) has been a promising approach for improved coverage and throughput. Most existing work assumes the ideal channel estimation, which can be challenging due to the high-dimensional cascaded MIMO channels and passive reflecting elements. Therefore, this paper proposes a deep denoising neural network assisted compressive channel estimation for mmWave IRS systems to reduce the training overhead. Specifically, we first introduce a hybrid passive/active IRS architecture, where very few receive chains are employed to estimate the uplink user-to-IRS channels. At the channel training stage, only a small proportion of elements will be successively activated to sound the partial channels. Moreover, the complete channel matrix can be reconstructed from the limited measurements based on compressive sensing, whereby the common sparsity of angle domain mmWave MIMO channels among different subcarriers is leveraged for improved accuracy. Besides, a complex-valued denoising convolution neural network (CV-DnCNN) is further proposed for enhanced performance. Simulation results demonstrate the superiority of the proposed solution over state-of-the-art solutions.