面 by itself means "face", while 白 by itself means "white". How did these two words combine together to mean "interesting"?
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According to 語源由来辞典 ( http://gogen-allguide.com/o/omoshiroi.html ), 「面白い」 is originated from 「面白し」. 「面」 used to mean "a sight/view" (the source says the front of eyes) and 「白い」 used to mean "bright and clear." Then 「面白し」 later came to mean "a light/bright sight/view" and then later "a beautiful sight/view". It further came to mean "fun" or "comfortable", which represents a pleasant feeling.
For your information, "interesting" better translates to 「興味深い」 to be accurate although it is often roughly translated as 「面白い」. 「面白い」 has several meanings with different nuances.