Counterspell interrupts, but does not prevent unit from casting that school of magic for 10 seconds.

The tooltip for counterspell states: 

"Counters the enemy's spellcast, preventing any spell from that school of magic from being cast for 10 sec.  Generates a high amount of threat"

Testing on the Defias Pillager's in Moonbrook.   When counterspell is cast, while the Pillager is in the process of casting a fireball, it does interrupt that cast, but they start casting another fireball within 1 second.