Effective communication requires good speech perception abilities. Speech perception can be assessed with behavioral and electrophysiological methods. Relating these two types of measures to each other can provide a basis for new clinical tests. In audiological practice, speech detection and discrimination are routinely assessed, whereas comprehension-related aspects are ignored. The current study compared behavioral and electrophysiological measures of speech detection, discrimination, and comprehension. Thirty young normal-hearing native Danish speakers participated. All measurements were carried out with digits and stationary speech-shaped noise as the stimuli. The behavioral measures included speech detection thresholds (SDTs), speech recognition thresholds (SRTs), and speech comprehension scores (i.e., response times). For the electrophysiological measures, multichannel electroencephalography (EEG) recordings were performed. N100 and P300 responses were evoked using an active auditory oddball paradigm. N400 and Late Positive Complex (LPC) responses were evoked using a paradigm based on congruent and incongruent digit triplets, with the digits presented either all acoustically or first visually (digits 1–2) and then acoustically (digit 3). While no correlations between the SDTs and SRTs and the N100 and P300 responses were found, the response times were correlated with the EEG responses to the congruent and incongruent triplets. Furthermore, significant differences between the response times (but not EEG responses) obtained with auditory and visual-then-auditory stimulus presentation were observed. This pattern of results could reflect a faster recall mechanism when the first two digits are presented visually rather than acoustically. The visual-then-auditory condition may facilitate the assessment of comprehension-related processes in hard-of-hearing individuals.