How do editors publish in their own journals?
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.