So They Naturally Make A Good Team When Doing Things Even If We Don't Really See Them As A Trio - Tumblr Posts
Mimi notably never directly refers to Yamato over the course of both adventure and 02. However there IS an implication of interactions in the first half of the show.
Mimi is one of the youngest in the group. Though she and Koshiro are the same age, Koshiro's quiet serious nature and computer skills often lead him to be treated more seriously while Mimi's penchant for complaining (no matter how justified), makes her treated a little more like a junior. There's a hierarchy of protection, that Mimi sits only above Takeru for. Mimi, being on the younger side, is more free to complain about her situation. Sora clearly looks after Mimi as the senior girl, as does Joe as the oldest over all, but Yamato also seems to look after her, at least in the first half of the season, as an extension of looking after Takeru. For instance, very early in the series, Yamato advocated for taking a break, presumably on behalf of Takeru, but it was both Takeru and Mimi who were struggling. And in episodes 5, 7, and 19 Yamato seems to be tasked with looking after the younger kids, Takeru and Mimi, Koshiro sometimes, even if I don't think it was necessarily purposeful in 5.
As such while we don't see much of Yamato and Mimi directly interacting it does stand to reason that they get along and do work well together. Yamato is generally rather considerate of people's negative emotions, such as with how he treated Sora's breakdown in episode 26 and how he handled Mimi's graves early in the dark masters arc. I would imagine that Yamato is relatively tolerant of Mimi's complaining. Conversely I would imagine Yamato is someone who Mimi holds a lot of respect for.
As a side note, the fact Taichi leaves Hikari in Yamato's care I think also speaks to Yamato's unspoken role of "babysitter", the complimentary shield to the role of sword Taichi plays. Yamato's tendency to prioritize the group's well being, over Taichi's tendency to take initiative and confront enemies. It also of course makes sense in the context of their crests, Taichi is courage (to do things), and Yamato's is friendship (to look after people).
And of course on the other side we get Joe Taichi and Sora as a group, the initiative takers, the ones who are more likely to do a dangerous job. Joe who went out in episode 7, Taichi and Sora who went to find him. Those three were the ones dealing with Andromon while the others looked around the factory, and the ones who went in for Sora's crest. Koshiro goes either way depending on if his skills are necessary or not.