Usage patterns
お互いに〈動詞〉to do something to/for each other
Let's help each other out when we're in trouble.
お互いの〈事〉を理解するto understand each other's situation/feelings
We talked it out and came to understand each other's feelings.
お互いのためにfor each other's sake
For both our sakes, let's be honest with each other.
Expressions
困った時はお互い様we should help each other in times of need; we are all in this together