Board Game Arena

In co-op, when both players encounter the bandit and don't bribe, you have to engage him twice, once for each character, and he has double health both times
Is this on purpose, or is this a bug? Different from all the other monsters.

It's intentional and follows what's written in the rules because the bandit isn't a monster. Non-monster cards are encountered by both players separately, even if they have the possibility of turning into battle.