According to this article, the F-35B is scheduled to be able to carry 18,000lbs of bomb payload, which is more than the F-18 Hornet carriers. But it also goes on to explain the F-35B's mission a little better, too. At first it will go in with an internal payload (max 4,000lbs) to dismantle the air defenses, then come back with up to 18,000lbs fitted in additional external bays. I'm it can do SVTL with just internal payload, but it doesn't clarify whether it will be able to do that with its maximum external payload.
For reference, the Harrier II that the F-35B replaces can carry a maximum of 9,200lbs of ordinance. Either way, it looks like the F-35B is a substantial upgrade in payload, range, and capability over the Harrier II.