As far as I know, the model 60 came in 2 versions: the .38 with the 1 7/8 inch barrel, and the .357 with the 2 1/8 inch barrel (I have a .357).
They are J-frames, and while they made J-frames in Airlite and Airweight versions, I don't believe they were called the model 60. For example, my titanium is the 342ti.
Anyway, unless the barrel says .38 +p (or .357), I wouldn't shoot +p's out of it unless I got the OK from the factory.