This paper investigates the broadband channel estimation (CE) for intelligent reflecting surface (IRS)-aided millimeter-wave (mmWave) massive MIMO systems. The CE for such systems is a challenging task due to the large dimension of both the active massive MIMO at the base station (BS) and passive IRS. To address this problem, this paper proposes a compressive sensing (CS)-based CE solution for IRS-aided mmWave massive MIMO systems, whereby the angular channel sparsity of large-scale array at mmWave is exploited for improved CE with reduced pilot overhead. Specifically, we first propose a downlink pilot transmission framework. By designing the pilot signals based on the prior knowledge that the line-of-sight dominated BS-to-IRS channel is known, the high-dimensional channels for BS-to-user and IRS-to-user can be jointly estimated based on CS theory. Moreover, to efficiently estimate broadband channels, a distributed orthogonal matching pursuit algorithm is exploited, where the common sparsity shared by the channels at different subcarriers is utilized. Additionally, the redundant dictionary to combat the power leakage is also designed for the enhanced CE performance. Simulation results demonstrate the effectiveness of the proposed scheme.