You and your husband are visiting a couple that you haven't seen in a long time. You and the other woman have been talking together for a few minutes while your husband and the other man talk to each other. Your husband wants to re-join the conversation between the men and women, so he asks how you're doing. You say:
We've just been catching up with each other.
catch up with (someone)
When you "catch up with" someone that you haven't seen in a while, you find out information about how their lives have been lately. You do this by sharing stories and making small talk.
If it's already understood who you're catching up with, you can just use the phrase "catch up":
We're just catching up.
(someone) has been (doing something)
When you use "has been ___ing" or "have been ___ing", you are describing an action that started at some time in the past and has continued until now. But now that action is finished.
In the example above, the speaker and her friend "have been" catching up with each other. But now that part of the conversation is finished, because her husband has interrupted it. If she wanted to continue to catch up with her friend, she could say:
We're just catching up with each other.