My heroes definitely receive the damage. Are you sure your hero did not have a regeneration spell or talisman? The effects are applied at once. For example, if you have regeneration, two life shrines, and a berserker band, you will see only a "+2" float up at the beginning of your character turn.
By the way, you can look at the attack stat, and the band should give you a bonus to, for example, cutting. You can check that both in and out of combat.
