This is not an "odd" subject at all. In fact, it is quite a common happening on many trees. So much so that many new software programs actually have indicators for adoptive parents, step parents, and so on and so forth.

It's really up to you how you'd like to handle this.
One way is to put "See Notes" where the marriage data would be enterred on the tree and then to write whatever you'd like to record in the notes portion (including that they were not married).

Another way would be to make two different tree. Each would start with you, but only contain a paternal or maternal line. In other words you'd have two trees, but each with only "half" a tree.

The important thing is that you don't feel "singled out" or all alone in your situation. It's not really uncommon and it's nothing of which to be ashamed or self conscious. Ultimately it's our challenges that make us who we are and give us our strengths.

Good luck to you in your search!