I wouldn't worry about defining it. Labels can be useful for quick reference, but people tend to get stuck in them and start using them to take cues on how to behave. That's always seemed silly to me.
You and she sound more like close friends than romantic partners. "Like a sister" isn't how I would describe my girlfriend, even though our relationship is non-sexual. We have a romantic, loving emotional bond, just without the sex. So even if I were prone to using labels, I wouldn't call your situation an emotional triad. That would imply that you and she are romantically involved, and it doesn't sound like you are.
It's nice that you've found this connection and that things seem to be working well. Have you discussed how this changes the nature of your relationship? i.e., if you met a woman with whom you felt an emotional and sexual attraction, would your partner support this? Of course, there might be no need to have that talk until that actually happens (putting the cart before the horse and all that), but it might not be a bad idea to establish that what's good for the gander is good for the goose
