60A subpanel service - when does it trip?
The double pole common trip breaker will trip when either pole exceeds 60amps.  Double pole breakers are common trip, therefore if one side trips then both poles trip.

So  drawing .5 amps @120v on one leg, and 61 amps @120v on the other, is a trip condition--and because it's common trip, both sides will go off.  

However you could pull up to 60 amps on both lines, as long as 60 is not exceed on either.