Harvard's PEG program is a single PhD that combines courses and faculty from multiple departments and is designed as such. You take one set of core courses (depending on track) and one set of quals (depending on track). Most designed/official joint PhD programs are run this way.
There some ad-hoc joint PhD programs that are essentially two PhD's. At my school, a B-school student can do a joint PhD with a relevant Arts and Sciences program (or vice versa), but they have to take the cores for both, quals for both, electives must satisfy both, and the thesis requires 5 essays as opposed to the usual 3.