Passive damage skills and bonuses on weapons are applied separately, so each will have a chance to hit.

There is a possible problem when combining any 2 of the skills Frost on a weapon, Stun on a weapon and the passive Stun skill, which can occasionally cause an opponent's death animation to hang in mid air, so you do not get the experience points and they do not drop loot. An area effect skill that does not need a target, such as hell Spikes, can force the animation to end properly. Some people also found that sleeping or just waiting awhile also helped.