This paper introduces our approaches for the Mask and Breathing Sub-Challenge in the Interspeech COMPARE Challenge 2020. For the mask detection task, we train deep convolutional neural networks with filter-bank energies, gender-aware features, and speaker-aware features. Support Vector Machines follows as the back-end classifiers for binary prediction on the extracted deep embeddings. Several data augmentation schemes are used to increase the quantity of training data and improve our models' robustness, including speed perturbation, SpecAugment, and random erasing. For the speech breath monitoring task, we investigate different bottleneck features based on the Bi-LSTM structure. Experimental results show that our proposed methods outperform the baselines and achieve 0.746 PCC and 78.8% UAR on the Breathing and Mask evaluation set, respectively.