When you say triad do you mean a full triangle, with emotional and sexual relationship between all partners? Or do you mean a V?
The jealousy you are describing makes me think V.
In my experience, our triad functions such that we don't need to tell the others that such person will be there, because as each of us loves the other two, we are always happy to see that person.
For instance, if my husband plans to meet up with our girlfriend and invites me along, then she is always happy to see me too. This is the same for all of us.
We definitely view our relationship as shared between the three of us. This is not to say that we don't have individual relationships between each couple, just that those relationships are a subset of the larger triad relationship.
I find this mentality actually leads to each of us feeling more secure, to the point where we will actively 'give' time to a coupling. This way we each get alone time while also feeling like we are doing something nice for the other two. I know it sounds cheesy, but it works for us.
So, I think there is a happy balance we've found. Our commitment to the relationship tends to guide us in trying to make each person happy. If we were each committed to being half of two couples, then I don't think it would work as well for us. A triad bond is very unusual we find it needs to take the front seat in our emotional line up for the relationship to stay solid.