Some years after the defeat of the Angels, the prevention of the Third Impact, the disbandment of SEELE and the retirement of the Eva programme, Asuka and Shinji acknowledged their feelings for each other and moved in with each other... it was a (mostly) happy ending, but some things never change; they still fight every day, struggle to maintain a house, and Asuka is still the boss
But they love each other and make a show of that every night