It has nothing to do with white people's face, according to the ナ津ェナ陳ケ窶燃窶藩?スツォ窶弋 (Ethymology Dictionary). Following is what is explained in the entry 窶禿岩?昶?吮?堋「.
窶禿岩?昶?吮?堋「 omoshiroi (enjoyable, fun, interesting, funny, etc.)
The orignal form of this word is 窶禿岩?昶?吮?堋オ (omoshiroshi). This word had been used almost the same meaning as 窶禿岩?昶?吮?堋「 today since 窶敕イ窶卍ケナスナセ窶佚」ツ・窶愿樞?氾?スナセ窶佚」 Asuka/
Nara period (6th century~), and its origin is not clear.
The most compelling theory is that 窶禿 (omo) means "in front of one's eyes", and 窶昶??shiro) means "clear and light". From thesewords, 窶禿岩?昶?吮?堋オ (later 窶禿岩?昶?吮?堋「ツ) became a word to express the situation that the light, clear view (in front of one's eyes), which turned into the beauty of the landscape.
It evolved further to "delightful" "pleasant", and was used to express ones positive feeling in general.
面白い/おもしろい - 語源由来辞典