Supervised speech separation has achieved considerable success recently. Typically, a deep neural network (DNN) is used to estimate an ideal time-frequency mask, and clean speech is produced by feeding the mask-weighted output to a resynthesizer in a subsequent step. So far, the success of DNN-based separation lies mainly in improving human speech intelligibility. In this work, we propose a new deep network that directly reconstructs the time-domain clean signal through an inverse fast Fourier transform layer. The joint training of speech resynthesis and mask estimation yields improved objective quality while maintaining the objective intelligibility performance. The proposed system significantly outperforms a recent non-negative matrix factorization based separation system in both objective speech intelligibility and quality.