How to make character not to fall through the floor ?

I have one character and a basic level, both are mesh colliders. Level is mesh collider with convex.
It doesn’t matter how high I put the spawn point, the character just falls through the floor.
EDIT: I tried applying rigidbody to both plane and character, than character just lags in the same position, I mean you can’t move character but it just lags it goes up and down very fast, I don’t know how to say it in other words.

http://unity3d.com/learn/tutorials/modules/beginner/physics

If you define the collider as ‘Trigger’ then the object will fall down.