There are three general schools of thought about how parties and clients should interact with a mediator.
The Open Book Approach
The first school of thought is that the mediator should be privy to basically everything. I would call this an open book philosophy. The lawyer encourages the client to be open with the mediator about information and only occasionally interjects in sessions with the mediator.
The Guarded Approach
The second school of thought is that the mediator is a potential adversary and should be kept at bay. For example, I have had mediations where a lawyer tells me that I should not direct any comments directly to their client while we are in the same room; that everything should essentially go through the lawyer. In these cases, the lawyer frequently admonishes the client not to be candid with the mediator and requests that the mediator leave frequently.
The Hybrid Approach
The third school of thought is a mixture of the first two. The lawyer and the parties see the mediator as a means to an end and recognize that there needs to be some free dialogue to move the matter along.