Everyday speech perception is challenged by external acoustic interferences that hinder verbal communication. Here, we directly compared how different levels of the auditory system (brainstem vs. cortex) code speech and how their neural representations are affected by two acoustic stressors: noise and reverberation. We recorded multichannel (64 ch) brainstem frequency-following responses (FFRs) and cortical event-related potentials (ERPs) simultaneously in normal hearing individuals to speech sounds presented in mild and moderate levels of noise and reverb. We matched signal-to-noise and direct-to-reverberant ratios to equate the severity between classes of interference. Electrode recordings were parsed into source waveforms to assess the relative contribution of region-specific brain areas [i.e., brainstem (BS), primary auditory cortex (A1), inferior frontal gyrus (IFG)]. Results showed that reverberation was less detrimental to (and in some cases facilitated) the neural encoding of speech compared to additive noise. Inter-regional correlations revealed associations between BS and A1 responses, suggesting subcortical speech representations influence higher auditory-cortical areas. Functional connectivity analyses further showed that directed signaling toward A1 in both feedforward cortico-collicular (BS→A1) and feedback cortico-cortical (IFG→A1) pathways were strong predictors of degraded speech perception and differentiated "good" vs. "poor" perceivers. Our findings demonstrate a functional interplay within the brain's speech network that depends on the form and severity of acoustic interference. We infer that in addition to the quality of neural representations within individual brain regions, listeners' success at the "cocktail party" is modulated based on how information is transferred among subcortical and cortical hubs of the auditory-linguistic network.