Compensation for channel mismatch and noise interference is essential for robust automatic speech recognition. Enhanced speech has been introduced into the multi-condition training of acoustic models to improve their generalization ability. In this paper, a noise-aware training framework based on two cascaded neural structures is proposed to jointly optimize speech enhancement and speech recognition. The feature enhancement module is composed of a multi-task autoencoder, where noisy speech is decomposed into clean speech and noise. By concatenating its enhanced, noise-aware, and noisy features for each frame, the acoustic-modeling module maps each feature-augmented frame into a triphone state by optimizing the lattice-free maximum mutual information and cross entropy between the predicted and actual state sequences. On top of the factorized time delay neural network (TDNN-F) and its convolutional variant (CNN-TDNNF), both with SpecAug, the two proposed systems achieve word error rate (WER) of 3.90% and 3.55%, respectively, on the Aurora-4 task. Compared with the best existing systems that use bigram and trigram language models for decoding, the proposed CNN-TDNNF-based system achieves a relative WER reduction of 15.20% and 33.53%, respectively. In addition, the proposed CNN-TDNNF-based system also outperforms the baseline CNN-TDNNF system on the AMI task.