Living separately

"So what happens? We just carry on like this until we're old and grey, living separately, together yet apart. What about a future, our future? We can live together but still have our own independence. I wouldn't expect either of us to give up our freedom. I admire the person you are, not the person I want you to be."

What does the phrase in bold face mean? Does it mean that the couple live in separate rooms under the same roof?