First off, in many cases you can just reference the object inside your Angular controller:
myObject.data();
You don't want to do this because then you are adding an undefined dependency to your controller, and that will cause trouble when trying to unit test your code. I believe undefined dependencies can cause issues when it comes to code maintenance too.
You could also wrap your custom object in an Angular Service. Something like this:
angularApp.factory('myCustomService', function(){
return new myCustomObject();
}
);
Then you can pass this object into the controllers:
function myController($scope,myCustomService) {}
I have used this when dealing with JavaScript code generated by WebORB.