In our institute the professor dispatches papers to certain employees(research fellows/assistants who are graduates or have a PhD degree) for peer reviewing. The professor takes responsibility for the reviews, still I wonder if this is the way the review process is meant to be.
Without making it known to the journal that he is not actually writing the review it is (usually, as far as I know) not supposed to be like this.
Here is one example, a quote from the PLOS One reviewer's guidelines:
Reviewers are required to treat all submitted manuscripts in strict confidence and should not share information about submissions with any other parties unless previously agreed with the editor. The involvement of a third party in the review must be declared at the time of the submission of the review.
If you ask the editor before you are sharing the publication with someone else, it can be okay. I have been "co-reviewing" with someone else (not my supervisor at that time), which was known to the editor and our names were both attached to the review.