Thank you all for your advice so far! It has given me a lot to think about and I will now clarify some things.
Firstly I have met with his fiance and she knows everything about our relationship. There aren't many rules that have been laid out between us but one of the major ones is honesty. I met her briefly on our first date together and made sure to verify with her that everything was alright and that she knew what was going on. She seemed perfectly fine with everything and even told me to calm down and relax some.
As for what our relationship actually is I was kind of confused at first too. We talked it over though and decided that girlfriend/boyfriend would be the best description. You see his fiance and him had been dating for three years long distance while they each continued to date and see other people until about a year ago when they moved in together. Since then they have only been swinging so I guess I can understand why there has been some insecurity.
While this relationship has caused me some stress I have learned a lot about myself and gained some much needed confidence. I'm also learning more about what it means to be in a relationship and while ours will eventually come to an end I don't think I'll have any regrets.