Historically, I have always had the Audit Committee approve their charter, audit policy, audit pre-approval policy, meeting minutes, audit schedule, Sox key controls, annual financial statement (before published), and external auditors. The charter and policies roll up to the Board for approval. The Audit Committee meeting minutes also are included in the Board packet for their awareness.
Many things are presented to the Audit Committee but they do not require their approval however they are documented in the meeting minutes. Examples include ALLL calculation and risk assessments.
I don't think their is a right way or a wrong way. You just want to make sure you are providing your Audit Committee everything they need to do a good job for your bank. And above all be sure everything is documented in the meeting minutes.