You're exactly right that because of the pressure difference between the inside and outside of the plane there is a force trying to rip the airplane apart.

To answer your question, think about a balloon. The pressure difference will make a balloon first expand and then explode as you increase the pressure difference. The same thing would happen to a plane if the pressure built up enough. Because of the lives at stake (and the several hundred million a 747 costs) great care is made to keep the plane structurally strong enough to take that force.

Each part of the plane is designed to be strong enough to be stable despite the high pressure difference. Next time you fly, look at the thickness of the doors and windows. Both are significantly thicker than what would be in your house. Additionally they are made of special types of materials that are stronger than what you would find in most places.

Similar to an aquarium, which often have even greater pressure problems, high flying planes use thicker and a stronger type of glass to overcome the pressure. Planes will still expand slightly like a balloon, just not enough to make the plane crack open.

One example of this is the billion dollar stealth bomber. According to a friend's father who works for Lockheed, the plane doesn't fit all that well together on the ground. Yet once it gets to altitude, which is much higher than commercial planes go, the plane expands slightly causing all the pieces to fit together perfectly. If they didn't build it that way, when the plane expanded they could buckle off a few pieces.
Hope that answers your question.