Sorry Alex,
You are confused on this issue. It is up to the patient to decide who attends appointments with them. In my experience shrinks prefer to see someone close to the patient at least once in a while, simply as a way of verifying the patient's problems.
There is no issue at all relating to doctor/patient confidentiality as the patient has waived that issue by bringing someone in.
To Given,
The reaction of your parents is, sadly, quite common. You see, if they accept and admit you have depression, then they think they are judged as "bad parents". They are only listening for themselves and not you at all.
You need to see a therapist to talk this out, not someone who is in denial. And selfishly so. My father denied any responsibity from 1961 until his death last year. Never once admitted the slightest fault.