Midriff is the correct spelling of the noun meaning the middle part of the human body, especially the portion between the bust and waist. It comes from Old English, where the prefix mid- meant the same as it does today, and hrif meant belly. Midrift is not a dictionary-recognized word.
Example
Because spell check catches midrift, it appears more often in speech than in written English. It does pop up occasionally in news sources, though—for example:
Andy Warhol shows off the scars left in his midrift by Valerie Solanas. [Bloomberg]
The outfit showed off her toned midrift and long legs as she sang songs from her upcoming album. [Daily Mail]
But most major publications get it right—for example:
Two-piece styles that cover all but a sliver of your lower midriff are another option. [Wall Street Journal]
The corpse of one of Gaddafi’s men was sprawled there, blood covering his midriff and his combat trousers. [Guardian]
The 21-year-old showed his anger at a lingering tackle by Port Adelaide’s Kane Cornes on Saturday night by jabbing the veteran Power midfielder in the midriff. [Sydney Morning Herald]
