This idea is a part of my faith. I don't believe, however, that this was necessarily meant literally, at least in the way that most people think. I believe it means that we, like God, are made up of a trinity: heart, mind, and soul. I think that this is what Jesus means when He says that the greatest Commandment is to "Love your God with all your mind, with all your heart, and all your soul." In this statement, He is evoking our entire selves.
I think that Freud was on this same idea, although he missed the mark, when talking about our Id, Ego, and Super Ego. He got the three components, but did not capture their true natures.
Jesus's Commandment instructs us not only to be devoted to God, but to come to a unity within ourselves, something that is not easy to do. Rarely are our three components in agreement with each other. Some people mistakenly try to settle this conflict by forcing an aspect of themselves into the shadows, or nurture one aspect to the expense of the others. What we need to learn to do is listen to the needs of each part of our own trinity, bring them into agreement, and find a way for them to work together.
We are, each of us, three persons living as one.