I look at the asteroids mainly for karmic indications.
I look at Chiron as a "karmic" planet when doing a composite or synastry, because this planet tells what both are going to need to heal...and that comes from past lives or experiences as a child. Chiron is the asteroid that tells you the biggest challenge in your life...the lesson to be learned. But it is a lifelong "healing" that must be done. The energy from Chiron, depending on the house, sign, and aspects to other planets is one that is hard to overcome. For example, in your chart with the communication issues, even if the other person understands and is listening, the other will never FEEL like they are understood, because the problem isn't really listening or communication. The real problem is that one or both of you are looking to the other to HEAL an old wound...and that just can't be done. That kind of healing only comes from inside yourself, by yourself, by healing yourself. So, the wound never heals because each looks to the other to heal something that the other can't heal. I see this when one or both has felt that they weren't "listened to" at an important time in their life from an important person...that caused some trauma or deep emotional injury. Occasionally, I've seen Chiron in Gemini with stress aspects that have shown a physical speech impediment (not in your composite, though). But, I think you see why I'd call Chiron a karmic indication.
Another example (but not in your composite chart) is someone with low self-esteem who constantly needs someone to make them feel worthy. It will never happen because no matter how much love is given, the person will always feel unworthy until they learn to love themselves. That's the kind of energy Chiron gives.
The grand trine with your jupiter, venus, chiron would indicate that you two can help each other heal. If it were a square, or "T" or opposition, you two wouldn't be able to help each other much.
Although your composite chart has a lot of squares, the asteroids have trines and "softer" aspects, although some squares there, too. So, this is where I really wanted to concentrate my attention. Ceres is another. It shows how you two will nurture each other. Ceres is in a trine with the sun...so you two can help each other along in positive and caring ways. But, Ceres is also squared with saturn. So, there will be times when you will both withhold (deliberately or by circumstances) the nurturing that you each need...but again, it is that "push and pull" when you both want the other person to heal something that you each can only heal yourselves by your own meditation and work on yourself, not on the other.
The true node (moon) is in a trine with neptune. This is another aspect that tends to show some karmic influence. It shows a deep wisdom and good flowing energy emotionally. (Of course, the squares will modify this some).
Quaoar is another asteroid with some karmic significance. Quaoar is in opposition to Lilith (the dark moon). Quaoar is usually a generational planet, but it can also show your relationship to the "divine" and your concept of "god" or the "universe." Lilith is the influence that shows us where we need to "let go" and have faith. Can you see how these two asteroids, in opposition, is going to make this an issue for you two? and perhaps how you two can heal or help each other?
Whew! I'm chatty today. I really enjoy these asteroids and how they show karmic relationships. There are other indications of karma in charts, but that's about all for now.