'MinkExtension' has been just released which has additional services for Behat. This extension has 'Mink' instance for your 'FeatureContext' and 'SubContext'. UI testers would be happy now, as they don't need to create Mink instance every time in order to use Mink API's.
He points you to an example application you can use to follow along. He includes the commands needed to install the dependencies via Composer and get this extension working (note: it requires PHP 5.4 for some of the traits stuff. If you don't want to use that, comment out the "TraitedFeatureContext.php" file). Also included are the commands to execute the tests with a Selenium server and a list of a few handy new things this extension enables.