There's no way of having common law couples appear on their profiles the way husband and wife do. But there are a couple ways you can deal with this.
First of all, parents of a child don't have to be connected at all. You can just add them each as a parent of the child. So there's that option.
You can also link people as spouses, but hide the relationship. Then it won't say husband and wife on the profile page, but you'll still see the relationship on the edit page.
And lastly (and you should probably do this whichever method you choose), you can explain the nature of the relationship in the biography sections, with a link to the other person's profile.
I hope that helps!