That, my friend, is the $64K question.
Of course, those who stand on our side of the fence think that Heller does protect us from an AWB. Dianne Feinstein clearly does not. She stated in a recent exchange with Senator Cruz that "Heller clearly carves out three exemptions" (or something very similar) into which she thinks her AWB fits.
Whether or not Heller actually provides the protection we want it to will be a decision for the courts.
I'm a lawyer, but I'm not your lawyer. If you need some honest-to-goodness legal advice, go buy some.