HOW WE GOT A MOON

The moon was formed about 4.5 billion years ago. Simulations performed by researchers at Southwest Research Institute TM (SwRI) and the University of California Santa Cruz show that a single impact by a Mars-sized object in the late stages of Earth/ formation account for an iron-depleted Moon and the masses and angular momentum of the Earth-Moon system.

The "Giant Impact" theory has been know and accepted by scientists for more than a decade because it proves an explanation for the low density of the moon. About 50 million years after the birth of the solar system, a planet of the size of Mars collided with the proto-earth. At this time the Earth was in the latter stages of its formation and had about 90% of the mass it has today. Due to the enormous mass involved the collision must have been very energetic.
Most of the mass of the earth probably melted and major portions would have evaporated.
The debris from the collision formed a ring around the earth, out of which the moon was born.
Subsequently, the moon moved further away from the earth and slowed down the rotation of the earth. The processes are still on-going. You can read the rest of this at http://www.spaceref.com/news/viewpr.htlm?pic=5773

So that is why earth rocks from the asteroid bombardment 3.8 billion years ago will still be found on the Moon and why Mars rocks can be found on Earth from the same asteroid bombardment.