Frequency modulation features capture the fine structure of speech formants that constitute beneficial and supplementary to the traditional energy-based cepstral features. Improvements have been demonstrated mainly in GMM-HMM systems for small and large vocabulary tasks. Yet, they have limited applications in DNN-HMM systems and Distant Speech Recognition (DSR) tasks. Herein, we elaborate on their integration within state-of-the-art front-end schemes that include post-processing of MFCCs resulting in discriminant and speaker adapted features of large temporal contexts. We explore 1) multichannel demodulation schemes for multi-microphone setups, 2) richer descriptors of frequency modulations, and 3) feature transformation and combination via hierarchical deep networks. We present results for tandem and hybrid recognition with GMM and DNN acoustic models, respectively. The improved modulation features are combined efficiently with MFCCs yielding modest and consistent improvements in multichannel distant speech recognition tasks on reverberant and noisy environments, where recognition rates are far from human performance.