The balloon will never escape the atmosphere. It simply drifts higher until it either reaches neutral buoyancy, or pops. As the balloon rises, air pressure decreases. The result is that the gas inside the balloon is compressed less as the balloon rises, causing the balloon to expand.

In a flight like jgc's, the latex balloon expands until it pops. There are other balloons which can float at a steady altitude. One of these is called a "Zero-pressure Balloon." This balloon operates with a valve on the bottom. The helium will expand until it reaches this valve, then spill out. When the balloon loses helium, it loses lift. The valve will tend to dump helium until the balloon reaches neutral buoyancy. These balloons are so named because the pressure at the valve is the same as the ambient atmospheric pressure.

Another type of balloon is called a "Superpressure Balloon." These balloons maintain altitude by pressurizing internally. Unlike latex, these balloons stop stretching at a certain altitude. As soon as the balloon stops expanding, it maintains a constant volume. Buoyancy is based on the volume of fluid displace, so a pressurized balloon maintains the same altitude.

I work with a group of hackers attempting to cross the Atlantic Ocean using a Zero-pressure balloon. (http://www.whitestarballoon.com). A group of radio amateurs actually beat us to the punch (http://www.arrl.org/news/amateur-radio-balloon-flight-crosse...), their crossing was involved a large quantity of luck. We seek to develop systems and methods for engineering balloons capable of traversing large distances safely and reliably.