What Theocracity said.
Example: I think it's pretty easy to assume that Space Wolves will be able to get a Blood Angels detachment. Now, how could they interact?
A: Both count as the same army in any means. I can assign my Wolf Guard to join Death Company, my Blood Angels Scriptor can buff Grey Hunters with his new Rulebook-Psychic-Powers and my Thunderwolves benefit from Sanguiniary Priests.
B: They fight alongside, but are treated as two small armies in any means. Effects of the one do not affect the other army whatsoever. You basically fight with two smaller armies against one big army.
C: Somewhat in the middle.