How do editors publish in their own journals? I was invited to review a paper in which the journal's Editor-in-Chief is a co-author. I do not mind, but raised the question that this peer-review is no longer blind. The co-author can see who wrote the reports.

I do not say the editor takes advantage of his position, but the peer-review is not actually the same.
In such cases, the editor-in-chief should recuse himself from having anything to do with the review process. This gives the associate or deputy editor for the given paper essentially full control of the process. (In general, I don't think the editor-in-chief is aware of exactly who is assigned to which manuscript.)

One would hope that the editor-in-chief would know the quality and standards required to publish a paper in her own journal; however, should the paper fail to meet those requirements, you should, of course, call that out in the review.