The phrase "a mutuality" is correct and usable in written English.
It can be used to refer to a shared or reciprocal relationship or connection between two or more parties.
Example: "The success of the partnership relies on a mutuality of interests and goals between the two organizations."
Alternatives: "a reciprocity" or "a shared understanding".
There was a mutuality in the deal.
In conversations with the Sony executives, "a mutuality of opinion" was reached, Mr. DeBitetto said.
The use of a star's individual brand has met a mutuality of needs.
There is a mutuality and interdependence that is even more fundamental.
As with all effective relationships, there is a mutuality of interests that both parties have to respect.
Shuffle Gesualdo, Messiaen and Beethoven into just the right alignment, the series suggests, and you will find a mutuality not necessarily expected.
As Mr Blackburn puts it, lust involves a "pure mutuality", a "joint symphony of pleasure and response".
As The Times' Kenneth Turan wrote in his review: "'Breathe In' takes pains to emphasize that this is not the story of a predatory male or a scheming Jezebel but rather of a fatal mutuality of interest". If there's a single studio-made romance in the last 20 years that walks such a careful, human line, I can't remember it.
There is normally a beautiful balance, a delicate mutuality, between the frontal lobes and the subcortical parts of the brain that mediate perception and feeling, and this allows a consciousness that is free-ranging, playful, and creative.
Sade the philosopher (not the odious, whiny sex offender) embodies the reasons, or the principle of unreason, that make it not only quixotic but sentimental to undertake the redemption of lust as a virtue — as what Blackburn calls "a pure mutuality of pleasure," and Fisher, for her sins, "a form of exercise and self-expression".
These elements add up to a love built on a respectful mutuality.
