According to Vaeflare, a community manager on Blizzard forums, there are no plans for cross-play between Battle.net and PlayStation Network. This is the full quote:
“While we think cross-platform play would be awesome, there are currently no plans to allow connectivity between PlayStation Network and Battle.net (this is pretty standard for most games that have PC and console support). As a result, the characters on your Battle.net account and PlayStation account will also remain separate.
In terms of allowing an analog controller hookup for the PC, we don’t have any plans for that kind of support right now. Similarly, since Diablo III for console was designed with a controller in mind, the PlayStation version of Diablo III will not support USB mice or keyboards.”
What do you think about this news from Blizzard?