I just got my reentry permit today (took about 5 months from the time of application). It looks exactly like a passport:
it has white hard cover, a passport-like first page with my photo, name, date of birth, country of citizenship, expiration date (2 years from the date of issue), A-number and book number (like a passport number). On the opposite page there is a space for the signature and a long text saying that "... this permit is issued to the person named herein, an alien previously lawfully admitted to the United States for permanent residence, to re-enter the United States.."
The first two numbered pages have the headers "Admission Stamps". Then pages numbered three trough twenty two have headers "Visas".
The white cover page says:
"United States Department of Justice
Immigration and Naturalization Service
Permit to reenter the United States".
So the reentry permit is essentially of the same design as a passport and I know quite a few people who use it as such.
Interestingly, INS decided to assign me a middle name: they transliterated (surprizingly correctly, but preserving its Russian conjugated form with an -vich at the end) my patronimic from the title page of my Russian passport whose copy I submitted with the application, and put it under "middle name" rubric in the permit.