So the code you referred to is the Fan wood code. And the Section 3-3.5 noted above is a subsection of Chapter XXIII, but "customary household pets" is not defined. Though the section on Animals only discusses dogs and cats.
I looked into this again because I plan on starting beekeeping in...
Did you ever figure this out? Just moved to Scotch Plains (near Shackamaxon) and I was thinking about getting some chickens. Wondering if you've discovered anything else?