Well I just think that having a missile to attack the SM-3s is pointless, since you make things a lot easier by just letting the SM-3s target your sub-missiles instead. Why would you need to aim for a missile aimed at you? Just have the submunitions attack their targets and naturally the SM-3s will be spent trying to intercept those mssiles/bombs/whatevers. Just give the ship's radar/combat management systems more targets to deal with and force them to fire more SM-3s. Along the same principles as MIRV.
Because the mini-missile can't go very far.
Imagine, the ASBM have reentered the atmosphere on its descending phase during the terminal phase. Launching at that high point, the mini missile wouldn't have enough fuel to reach the ship.
Not to mention, the ship defense can distinguish the profile of a ASBM and the mini missiles, the SM-3 still can bypass the small one and will head straight toward the ASBM.