Midpoints are mathematical points, so there's no energy produced when these points aspect each other. In other words, midpoints are only triggered by personal planets or angles by transit or synastry.
That said, in your situation both persons will be triggered by the same transits at the same time with differing outcomes depending on the houses that the midpoints lie.
e.g.
A: sun/moon midpoints at 10 Libra in 5th house
B: sun/moon midpoint at 10 Libra in 8th house
If these two people are in a relationship (Libra) and T.North Node (the future) in Cancer (home and family) reaches 10 deg it will trigger both persons at the same time with a square (challenge, stressful event). Which could mean that A suffers a loss of a child (5th H) and the partner B suffers a death (8th H) of the same child.
OMG! This was a horrible example, I should have used a celestial body like Saturn in Cancer.
Thanks Osiris Wife. That helps.
Posted by: @vesta
What do you think about progressed sun moon midpoint's relationship with self and others? Is our inner marriage (or its needs) also evolving along with us? Is it also an indicator in predictive astrology?
I don’t know if our inner marriage necessarily evolves, maybe it does. Intuitively, I think what evolves is how we progress towards our inner marriage as promised in our natal chart, the blueprint. So for me, progressed or transit planets to n.Sun/Moon midpoint are more important.
For example, I’ve noticed that in the year in which a significant relationship starts the SR Moon is conjunct n.Sun/Moon midpoint. Also, the house of the SR Moon often describes, the activities or profession of the person the relationship will be entered with. If it’s romantic or other type of relationship, the rest of the SR will indicate so. I also stumbled on this recently, that if the SR Moon is VOC, the relationship will be significant leaving a lasting impression, but it will likely come to an end – it seems there’s something that culminates, as in karmic energy.
Transits to the n.Sun/Moon midpoint (hard aspects only 0-5°) will provide more information of the energy of the relationship e.g. Pluto will be intense, Saturn maybe binding and/or career related, Uranus might start and end suddenly or will be unconventional etc.
Since it takes two to have a relationship, both persons will have their n.Sun/Moon midpoint fired up, and at least one contact via synastry (also hard aspects only 0-5°). If it’s a double whammy in synastry, that’s gold!
@osiris-wife Seems like a once in a life-time type of thing. 
Thanks for the inspiration. I will keep an eye on the Sun-Moon midpoint for transits now.
I wonder if there are other midpoints that are as powerful for other aspects - Sun-Jupiter (new beginnings), Mercury-Moon (Total harmony) (Moon-Mars or Moon-Saturn) Parental archetype pairing.
Recently I started paying attention to Venus/Mars midpoint, sexual and creative expression. Also, I think Asc/Dsc midpoint is interesting; the totality of outward expression.
I think midpoints utilize planetary energy through the midpoint to act as one. They might form a conjunction, opposition or square with the midpoint.
As an example, I have two planets in early degrees of Scorpio and two planets in later degrees of Scorpio. The midpoint between them joins all of them together. I especially notice it now because of transiting Uranus in Taurus. It seems to create a stellium that experiences the Uranus transit as one.
In synastry, the same thing happens. Two planets from one person can work with planets from another using the midpoint even though they would be out of aspect otherwise.