{blackbabes} Janet Jackson and Jermaine Jackson -- Brother & Sister Face-Off [PHOTO

TMZ has obtained a photo of Janet Jackson and Jermaine Jackson in a heated exchange at the Jackson family home-- shortly after Sheriff's deputies responded to an alleged battery there on Monday afternoon.

In the pic, Janet and her brother Jermaine are in front of the Calabasas compound ... clearly engaged in a heavy conversation.

We're told the photo was taken within the same hour LA County Sheriff's deputies went to Katherine Jackson's home ... after someone inside accused someone else of a physical assault.

We do not know if Jermaine and Janet were involved in that dispute.

As we previously reported, Janet and Jermaine have a lot to discuss -- the letter they and 3 other siblings signed, demanding the Executors of Michael Jackson's Estate step down ... and Katherine Jackson's puzzling trip to Arizona.