Check the Node.js module documentation where require() is thoroughly explained.
http://nodejs.org/docs/v0.4.5/api/modules.html
As for your specifics:
Modules are cached after the first time they are loaded. This means (among other things) that every call to require('foo') will get exactly the same object returned, if it would resolve to the same file.
Hence, if you require('underscore') in both your parent library and './routes/document', only one instance of the underscore module will be loaded and hence. Both variables will be in fact the same object.
And by the way, you don't want to define variables in the global scope as it might generates side effects and potentially overwrite properties in other modules.
Finally, the util module provides an inherits method to subclass another constructor and inherit from its prototypes.
http://nodejs.org/docs/v0.4.5/api/util.html#util.inherits