Enderman will chase after endermites, even if they are in water. Then, once they are killed, the enderman will stay in the water being damaged.

If an endermite it pursuing the player and they go into water, not only will they sink to the bottom and drown, but enderman will follow them. The enderman starts to take damage wanting to kill the endremite. However, once the endermite is killed the enderman will stand in the water getting hurt, standing there not moving, until provoked or a random teleport.