The couple were snapped stocking up on a few essentials at the supermarket, reported E!Online.
Joseph, 33, looked relaxed and comfortable as photographers took pictures of the pair's rare public outing.
McCauley donned a purple printed romper and brown leather boots, while the actor was dressed casual in a baseball cap, a three-quarter sleeve tee and black jeans.
The 'Dark Knight Rises' star is yet to divulge details about his girlfriend. He did confirm their relationship in September.
"I have a girlfriend but I tend not to really like to talk about it in public. The girl that I'm with, she really doesn't want to be a part of that," Joseph had said at the time.
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