You asked

I know that my partner and I will fight, but is there such a thing as fair fighting?

No matter how much you and your partner love each other, and no matter how perfect your relationship seems there will come a time when you will disagree about something and have a fight. However, there is an effective way to fight that will be constructive in helping your relationship to grow.
You need to agree on how to handle your disagreements. This could be that you make a decision to never go to bed angry at each other, or that, should it look like an argument could start, to leave and take a walk until the anger passes.
It is very important that you show respect for each other even when you disagree. Do not belittle each other, blame each other, or involve your children in your fights. Most times, your arguments will be about the same things every time. The trick is to not bring up past arguments, but fight about the immediate issue instead.
When you and your partner are having an argument and things begin to get somewhat heated, then take a break from the fight before you start saying things that you do not really mean. Once you have taken time to cool off, get back together and discuss how to resolve the issue and how you can fix the problem together.

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