The boundary between our atmosphere and outer space is about 100km out from the surface of the earth! The Earth's atmosphere is actually divided into several layers. The lowest layer is the troposphere and extends to 20km. The next layer is the stratosphere which contains our ozone layer and extends to 50km. Beyond this is the mesosphere which is where most meteors burn up and extends to 85km. The thermosphere is next and extends out to 690km! This is where the space shuttle hangs out and the boundary between the atmosphere and outer space is within this layer. Beyond this lie the ionosphere and exosphere.

There is no space between the surface of the Earth and the atmosphere.

Also, here is no definite boundary between the atmosphere and outer space. It slowly becomes thinner and fades into space. Three quarters of the atmosphere's mass is within 11 km of the planetary surface. The following link may also provide some information to help answer this question.