Elon and Amber issued a joint statement Friday morning calling out media outlets that have mischaracterized their relationship. As for what their relationship is ... well, based on the statement, it's complicated.

Here's what they say ... "The distance has been really tough on our relationship, because we haven't been able to see each other much. All relationships have their ups and downs, of course."

The statement goes on ... "We would like to state directly that we have the utmost respect for one another, and it would be troubling if anyone had the impression that we thought otherwise."

It ends this way ... "It is worth bearing in mind that events are always amplified and dramatized in a high profile relationship, whether the people involved like it or not (and we definitely don't). The reality is that this is just a normal relationship with a giant magnifying glass applied."

BTW ... Elon was spotted Thursday at a coffee shop in Australia.

So, on a break?