There are a few red flags for me about your post. I agree with Ari that a search on here for unicorns would be useful to read what others have discussed before.
The red flags for me around unicorn hunting are that couples think they are a hot commodity because they enjoy THEIR relationship. Your relationship rocks because its just the two of you, adding another would mean your relationship would not be the same, it would be a relationship of three. Another person means another relationship, not the same one with a person added on. I would suggest thinking of your venture as such so as to not think of looking for another as you would look for a puppy. Very different.
Red flag two is that you seem to be looking for something long term. Long term and traids are very rare and don't usually come about by a couple searching for someone to add to their lives. More over they just happen and emerge out of three separate people. Its probable that your relationship will be based on sexual NRE and only last for a short time before someone feels left out and the triad breaks into a vee instead. What is likely is that the new woman and the man find a deeper compatiblutt and you will be disconnected from that. Its likely that he will become the hinge of a vee or one person will break off and go it alone.
Anyway, not great news, but it has been done to break through the odds. Just know that your thoughts on this are a dime a dozen and might be great in fantasy, but in reality a whole lot of hardship and work.
Hope some reading helps out things into perspective.
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