Here is a solution that I use to make real HTTP calls when I'm using ngMock for unit tests. I mainly use it for debugging, working through the test, getting JSON examples etc.
I wrote a more detailed post about the solution on my blog: How to Unit Test with real HTTP calls using ngMockE2E & passThrough.
The solution is as follows:
angular.mock.http = {};
angular.mock.http.init = function() {
  angular.module('ngMock', ['ng', 'ngMockE2E']).provider({
    $exceptionHandler: angular.mock.$ExceptionHandlerProvider,
    $log: angular.mock.$LogProvider,
    $interval: angular.mock.$IntervalProvider,
    $rootElement: angular.mock.$RootElementProvider
  }).config(['$provide', function($provide) {
    $provide.decorator('$timeout', angular.mock.$TimeoutDecorator);
    $provide.decorator('$$rAF', angular.mock.$RAFDecorator);
    $provide.decorator('$$asyncCallback', angular.mock.$AsyncCallbackDecorator);
    $provide.decorator('$rootScope', angular.mock.$RootScopeDecorator);
    $provide.decorator('$controller', angular.mock.$ControllerDecorator);
  }]);
};
angular.mock.http.reset = function() {
  angular.module('ngMock', ['ng']).provider({
    $browser: angular.mock.$BrowserProvider,
    $exceptionHandler: angular.mock.$ExceptionHandlerProvider,
    $log: angular.mock.$LogProvider,
    $interval: angular.mock.$IntervalProvider,
    $httpBackend: angular.mock.$HttpBackendProvider,
    $rootElement: angular.mock.$RootElementProvider
  }).config(['$provide', function($provide) {
    $provide.decorator('$timeout', angular.mock.$TimeoutDecorator);
    $provide.decorator('$$rAF', angular.mock.$RAFDecorator);
    $provide.decorator('$$asyncCallback', angular.mock.$AsyncCallbackDecorator);
    $provide.decorator('$rootScope', angular.mock.$RootScopeDecorator);
    $provide.decorator('$controller', angular.mock.$ControllerDecorator);
  }]);
};
Include this source file after ngMock, for example:
<script type="text/javascript" src="angular.js"></script>
<script type="text/javascript" src="angular-mocks.js"></script>
<!-- this would be the source code just provided -->
<script type="text/javascript" src="ngMockHttp.js"></script>
How to write the test?
  describe('http tests', function () {
    beforeEach(module('moviesApp'));
    var $controller;
    var $httpBackend;
    var $scope;
    describe('real http tests', function() {
      beforeEach(angular.mock.http.init);
      afterEach(angular.mock.http.reset);
      beforeEach(inject(function(_$controller_, _$httpBackend_) {
        $controller = _$controller_;
        $scope = {};
        $httpBackend = _$httpBackend_;
        // Note that this HTTP backend is ngMockE2E's, and will make a real HTTP request
        $httpBackend.whenGET('http://www.omdbapi.com/?s=terminator').passThrough();
      }));
      it('should load default movies (with real http request)', function (done) {
        var moviesController = $controller('MovieController', { $scope: $scope });
        setTimeout(function() {
          expect($scope.movies).not.toEqual([]);
          done();
        }, 1000);
      });
    });
  });
How it works?
It uses ngMockE2E's version of $httpBackEndProvider, which provides us with the passThrough function we see being used in the test. This does as the name suggests and lets a native HTTP call pass through.
We need to re-define the ngMock module without its fake version of the $BrowserProvider, since that is what prevents the real HTTP calls in unit tests that use ngMock.