It would be rare in this day and age for PC and console gamers playing the same game to be able to connect up and play together and Blizzard has confirmed that this will not be possible in Diablo 3.
With the PC version utilising Battle.Net and the PS3/PS3 version utilising the Playstation Network, the two will simply not talk to each other. Blizzard posted:
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.
Why anyone would want to use a console controller on the PC version of Diablo 3 is beyond but I can understand a console gamer wanting to use a mouse. Having said that, the PS3/PS4 version does have a completely different interface design so it probably wouldn’t work that well with a keyboard and mouse.