When I DM, an invisible character who isn't stealthed is fair game (though, admittedly, not a very attractive target due to the -5 penalty).
No one knows the location of a hidden character, so he gets ignored unless perhaps the enemy has a large area attack and an axe to grind. Since moving more than 2 squares applies a -5 penalty to your Stealth check, it's not unreasonable (IMO) to target the origin square with a burst 2 attack (keep in mind that area attacks ignore the -5 penalty from total concealment).
Also, you may want to note that Eyebite will not allow you to become hidden under most circumstances. Eyebite only causes you to become invisible against one target. However, you need total concealment against all enemies in order to become hidden (any enemy who sees you can point out your square to his allies as a free action, which can be done even when it isn't his turn). This also applies when your Stealth check beats the passive Perception of some, but not all, enemies.
If you find that being attacked even while hidden is a problem, one possible solution would be to use several decoys to obscure your position. Take several tokens. Write your character's name on one and decoy on the rest. When you become hidden, place the tokens in legal spaces face down (so if you didn't take the -5 Stealth penalty, put them within 2 squares of your starting position). When the DM wants to attack you, he has to pick a token and attack it (unless it has your name on it, the attack automatically misses). Note that this will probably slow down game play somewhat, if you use steath regularly, so I'd only use it if you feel it's truly a necessity.
In 4e, it's generally quite difficult to make yourself effectively invulnerable for an extended period of time.