Recently, the reconfigurable intelligent surface (RIS) aided communication system has emerged as a promising candidate for future wireless communications. The existing channel estimation methods for RIS-aided millimeter-wave systems assume that the RIS is ideal without blockage. However, in practice, RIS may be blocked by the rain, snow, or dust, which will cause absorption and scattering of the incident/reflected signals and change the channel characteristics. In this paper, we formulate the system model of RIS-aided multi-user communications considering the blocked RIS. Then, we propose a variational Bayesian based channel estimation algorithm that is robust to RIS blockage, where we can simultaneously estimate the channel information and the RIS blockage. Simulation results demonstrate the superior performance of the proposed algorithm to existing ones.