Central processing of interaural correlation (IAC), which depends on the precise representation of acoustic signals from the two ears, is essential for both localization and recognition of auditory objects. A complex soundwave is initially filtered by the peripheral auditory system into multiple narrowband waves, which are further decomposed into two functionally distinctive components: the quickly-varying temporal-fine structure (TFS) and the slowly-varying envelope. In rats, a narrowband noise can evoke auditory-midbrain frequency-following responses (FFRs) that contain both the TFS component (FFRTFS) and the envelope component (FFREnv), which represent the TFS and envelope of the narrowband noise, respectively. These two components are different in sensitivity to the interaural time disparity. In human listeners, the present study investigated whether the FFRTFS and FFREnv components of brainstem FFRs to a narrowband noise are different in sensitivity to IAC and whether there are potential brainstem mechanisms underlying the integration of the two components. The results showed that although both the amplitude of FFRTFS and that of FFREnv were significantly affected by shifts of IAC between 1 and 0, the stimulus-to-response correlation for FFRTFS, but not that for FFREnv, was sensitive to the IAC shifts. Moreover, in addition to the correlation between the binaurally evoked FFRTFS and FFREnv, the correlation between the IAC-shift-induced change of FFRTFS and that of FFREnv was significant. Thus, the TFS information is more precisely represented in the human auditory brainstem than the envelope information, and the correlation between FFRTFS and FFREnv for the same narrowband noise suggest a brainstem binding mechanism underlying the perceptual integration of the TFS and envelope signals.