Unfortunately it is almost as bad as being fired, and will probably come out on a background check. You may be able to overcome the situation if you spin it into a learning experience, but don't lie about it, that will doom you.
You might be able to come to a 'gentlemen's agreement" with your former employer: you don't sue them or make trouble for them, they give you a decent recomendation.
Note: Have your girlfriend pretend to be a reference checker for some generic aviation company and call your previous employers to do a "background check". See what you come up with...if there are any problems, maybe you can go back and smooth it over.