This is an example of flapping (see Wiki). In American English, in certain positions /t/ and /d/ can get replaced with the voiced alveolar flap sound [ɾ], and (as here) /nt/ can get replaced with the nasalized flap [ɾ̃], which can also be a realization of /n/. This can create interesting sets of homophones: for some American speakers, winner and winter sound exactly alike.
This generally occurs at the end of a stressed syllable when it is followed by an unstressed one, so it applies to antihistamine but not to antithesis. The rules are a bit more complicated than that, particularly when flapping occurs on word boundaries; that Wiki page goes into some more detail.