In the first season, Olivia and Kathy did not share any scenes together. But they have mentioned one another and must've already met off screen. Olivia knew that Kathy was really the 'man' of the house because Elliot's never there. Late one night, Kathy found Elliot and tried to make conversation with him but he was quiet. She asked Elliot if he talked to Olivia about work- he does- she's his partner.
In the fourth season, Elliot trusted Olivia with his credit card to get a birthday present for Kathy. Kathy went to see Elliot, bringing him dinner. Although they were in the same room together, Kathy and Olivia did not get a chance to talk (or share the same screen).
In the fifth season, Olivia asked Elliot about Kathy drinking alcohol while pregnant after learning about Fetal Alcohol Syndrome (FAS). Kathy had given Elliot four (later five) healthy children, he'd trust her to make the decision.
In the sixth season, Olivia was shocked by hearing from attorney Lorna Scarry that Kathy had filed for legal separation and moved in with her mother, taking the children with her. The job was making Elliot difficult to live with but he eventually started to fall apart at work, refusing to go home to an empty house.
In the seventh season, Elliot told Olivia not to call Kathy after he was shot; she started divorce proceedings a couple of weeks ago.
In the ninth season, Elliot already moved back home. Olivia accompanied Elliot to his house when their suspect Janis Donovan was holding Kathy hostage with a knife. In another episode, after interviewing parents of disabled children, Olivia could see Elliot being worried about Kathy and the baby as she was over 40 years of age. When Elliot was seriously injured and in the hospital, he woke up Kathy notified Olivia and the nurse. Elliot recovered.
In the twelvth season, Kathy answered Elliot's cell phone- she saw that it was Olivia and referred her as his office wife. Kathy called Olivia 'Liv'. Other than talking to each other on the phone, Olivia and Kathy shared no scenes together. It was Christopher Meloni's final season.