How does this work: we are only dating each other, but we are not in a relationship?

He calls me his baby and says that I am his and no other guy can have me. We talk to each other like we are together...we say we miss each other and stuff...and we don't date other people. At work a girl gave her number to our boss and told her to give it to him and he told our boss to throw it away. He has thrown numbers away since we started talking. He gets jealous if I talk to other guys and I get jealous if he talks to other girls, but we aren't interested in anyone else. We talk everyday and see each other almost everyday. If we don't though we feel a little off. He treats me the same way in public that he treats me in private. He holds my hand, loves on me, puts his arms around me...he is just sweet and attentive. I can't call him my boyfriend because he said that we can't be together right now (he was cheated on by his last girlfriend who was his fiance and he said that he is still in love with her...) but he also said that he could see himself loving me. He tells me that he really likes me a lot. We have a ual relationship. So...what are we? We have to be more than friends with benefits because it is not just physical. If we are not in a relationship, what are we?