Knowing the geometrical and acoustical parameters of a room may benefit applications such as audio augmented reality, speech dereverberation or audio forensics. In this paper, we study the problem of jointly estimating the total surface area, the volume, as well as the frequency-dependent reverberation time and mean surface absorption of a room in a blind fashion, based on two-channel noisy speech recordings from multiple, unknown source-receiver positions. A novel convolutional neural network architecture leveraging both single-and inter-channel cues is proposed and trained on a large, realistic simulated dataset. Results on both simulated and real data show that using multiple observations in one room significantly reduces estimation errors and variances on all target quantities, and that using two channels helps the estimation of surface and volume. The proposed model outperforms a recently proposed blind volume estimation method on the considered datasets.