"in mutual interest" is correct and can be used in written English.
It is used to describe a situation in which two or more parties have a common goal or benefit from reaching an agreement. For example: "The two companies signed the contract in mutual interest."
"Let us work together in mutual interest and for progress and prosperity of our great countries".
"It is in mutual interest of both the people of the Republic of Ireland and those of the United Kingdom that there should be civilised relations between us.
"Both the DPRK [North Korea] and the US affirmed that it is in mutual interest to ensure peace and stability on the Korean peninsula, improve the relations between the DPRK and the US, and push ahead with the denuclearisation through dialogue and negotiations," it said.
The ardent affair between one of Europe's tiniest countries and its giant ally is grounded in mutual interests.
"The production of a film of such a character will arouse very bad feeling in Germany against the producing company and may lead to serious difficulties which should be avoided in mutual interests," he wrote, by which he meant that the film, at his suggestion, could be banned in Germany.
Letting Mr. Boehner regain some of his footing may be in their mutual interest in the short term.
That is why it is in our mutual interest to achieve a global accord in which we agree to take certain steps, and to hold each other accountable for our commitments.
And he contended that it is "in our mutual interest to achieve a global accord in which we agree to steps, and to hold each other accountable for certain commitments".
When Eurobarometer pollsters asked Turks whether membership was mainly in their interest, the EU's interest or in the mutual interest of both, the largest block of respondents (34%) thought the main beneficiary would be the EU.
For that reason, Greece should firstly try to open a dialogue with Εurope, in a way that stresses the fact that altering these policies is in our mutual interest.
