phpspec unit testing - using ioc / service registry for delivering the concrete class to test

I am new to testing and I'm not sure I go about this the right way:

I want to not to do a unit test on a specific class but on whatever class get resolved out of my ioc container. In the ioc container I bind my interfaces to concrete classes, like so:

Example (I'm using Laravel 5):

// in a service provider
public function register(){ 

    $this->app->bind('FooInterface', function() { 
        return new SomeConcreteFoo; 
    }); 
 }

Then I want to write unit test against FooInterface and not SomeConcreteFoo which could be swapped out with some other class at a later point.

The reason I want to do this is that it seems to me that the relevant testing should target whatever my ioc container returns, since that is what I'll be using in the application. It also seems to me that the testing should be done on the interface level, since that is where I define the expectations the rest of the app will have to my class.

I'm having a hard time finding any information on how to do this, which suggests to me that I might think about this the wrong way. For instance maybe what I'm trying to accomplish is more like an integration test rather than a unit test.

So the first question is: am I thinking about testing this the right way? in case I'm not - do you have any suggestions regarding best practice for an alternative test path.

The second question: In case my thinking is sound - how do I setup phpspec to make use of the Laravel IOC container, so that I can test against whatever the IOC returns..