It was their seventh year. They were doing rounds, since they were the Heads now. Yes, they also didn't believe it. I mean, they believed Lily would be Head Girl, but James as Head Boy? Who would have seen that coming? They thought maybe Dumbledore had gone a bit crazy, but the truth was, James had matured (finally) and he was worth the title.
They were already getting tired from walking around the school, looking for kids out of curfew. They kept a civilized conversation. James and Lily weren't the same James and Lily from two years before. There weren't daily yelling between them and James didn't ask Lily to go out with him at every second anymore. The only fights that they had nowadays were regarding their Heads' duties. And even those were minimum and settled quickly. They could actually consider themselves to be friends, much to the surprise of the whole school.
And as their round time was nearing its end, the two Heads entered another empty room that was never used for any class. But that room was different. Not even James remembered exploring it. The room was empty, no students out of curfew, just a very old looking mirror standing in the middle of the room. The mirror had weird and illegible inscriptions in its boards, which they didn't give much thought to, as they only looked at the two of them in the mirror for a few moments before turning around and leaving the room.
Neither of them saw anything different. They both judged the mirror to be just a normal mirror as they only saw their reflection on it. The two of them standing side by side. Neither of them ever found out that that had been the Mirror of Erised. Neither of them ever found out that the Mirror was telling them that they were each other's biggest desires. But that was okay, because they found out by themselves later on.