we try to communicate more openly and honestly with each other
I think this is the key to having a good relationship with another person, and it works with all kinds of relationships, whether romantic, friendship, or simply work-related. And I agree with you, I think that the "willingness to compromise" also plays an important role. Of course, a solution will not always be found, and it is okay to agree to disagree, but even then an agreement can be reached and all the people involved are respected.
For me I believe the only way to settle misunderstanding is to compromise and both agree.