You can hear a genuine three-syllable "Mom" in the opening title sequence of the kids' television show, "Phineas and Ferb." The character Candace says,
"Mmm-MO-om, Phineas and Ferb are making a title sequence!"
The pitch matches the stress, low-high-low. The first syllable is brief but clearly discernible. I suppose one could argue that it's not a true syllable, since it lacks a vowel, but the word is certainly three distinct beats.
A pitch track of the "Mom!" part shows that there are indeed three notes, though not really three syllables (or three "beats"), since the first pitch is clearly limited to the initial [m] (just as Brooke describes it).
(Click on the image for a larger version. The mis-tracking of pitch at the edge of the high note may be in some sense real, being caused by some laryngealization that may actually cause temporary period doubling.)
The pitches are roughly 250, 614 and 464 Hz, which (relative to A 440) are approximatly b, d#", and a#'. (Given those values, the first note is about 18 cents sharp relative to a concert A, the middle note is about 22 cents flat of tempered concert D#, and the third note is about 8 cents flat relative to tempered A#. But different choices of measurement points or regions would give different numbers.)
Here's a plot for the "Phineas and Ferb are making a title sequence!" part of the complaint, where there are (what I take to be) two more replications of the same pattern:
Contrary to the opinions of several commenters on the earlier post, there's no sign of a rise on the final note, either in the "Mo-om!" phrase or in the "…title sequence" phrase. That agrees with my own impressions about this pattern. But they may be right about their own variants — or in fact, this instance may be closer to the traditional vocative intonation, since it represents appeal to a distant mother, rather than reproof of a present one. I repeat my earlier call to send me audio clips, either of other renditions in popular culture, or in your own performance.