Recent studies in neural network-based monaural speech separation (SS) have achieved a remarkable success thanks to increasing ability of long sequence modeling. However, they would degrade significantly when put under realistic noisy conditions, as the background noise could be mistaken for speaker's speech and thus interfere with the separated sources. To alleviate this problem, we propose a novel network to unify speech enhancement and separation with gradient modulation to improve noise-robustness. Specifically, we first build a unified network by combining speech enhancement (SE) and separation modules, with multi-task learning for optimization, where SE is supervised by parallel clean mixture to reduce noise for downstream speech separation. Furthermore, in order to avoid suppressing valid speaker information when reducing noise, we propose a gradient modulation (GM) strategy to harmonize the SE and SS tasks from optimization view. Experimental results show that our approach achieves the state-of-the-art on large-scale Libri2Mix- and Libri3Mix-noisy datasets, with SI-SNRi results of 16.0 dB and 15.8 dB respectively. Our code is available at GitHub.