What does "two-way justice" mean? Can I use it to describe a relationship between two people (without considering the role of gender) in which there is a complete equality in behaviors and reactions?
Just and justice, at least in US use, tend to be restricted to talk about law, or systems like the legal system. They are not ordinarily be used with respect to personal relationships; there, fair and fairness are more likely.
Better terms for what you are trying to express might be mutual fairness or mutual respect.