Percy and Annabeth often find themselves in situations where they have to protect mortals from the threats of the demigod world. So in their interactions, they may seem like guardians. They might give warnings to mortals who are unknowingly close to danger. For example, if there's a monster lurking near a mortal neighborhood, they'll try to get the mortals to stay indoors without scaring them too much. And they also might form friendships with some mortals, but always with the understanding that their world is different and they can't fully disclose everything.
They interact cautiously. Since they are demigods and their world is full of secrets, they don't want to expose themselves. Percy might be a bit more laid - back in his interactions, cracking jokes with mortals while still being vigilant. Annabeth, on the other hand, is more calculating. She'll study the mortals first to see if they can be trusted.