You can also add the example of the now defunct Affliction organization and Strikeforce co-promoting.
Arlovski fought on the Kimbo CBS card against an Strikeforce fighter. He was on "loan" from Affliction which was his organization at the time. Babalu (Strikeforce) fought on Affliction cards against Affliction fighters.
Just another example of fighters from different organizations fighting, which was your inital question.
Chuck v. Rampage (after he beat Overeem) was the most notable exampe since it was the UFC vs. Pride, both were major organizations and major competitors, and major stars for each organization (like Superman vs. Spiderman).