I find my rosters consist of about 75% cargo flying and, recently, that figure has been even higher (around 80%). One of the problems is, predictably, the JCAB and it's insistence (so we're told anyway) that training be carried out on pax flights and not cargo. Take those trips from the list, the pax trips that must be flown by the over-60 Japanese 'career' pilots and the pax trips that are used for checking and the number of cargo trips soon mounts for the standard line pilot. I agree with TD that, for the pilots, combining the two companies was ONE of the worst thing they've done but I don't think they're going to change back any time soon.
As far as consecutive nights are concerned, the average cargo patterns seem to consist of two and then a reversal to a day flight to get back to NRT. There are plenty of three night trips floating around but it's likely that you'd only see one of these on your roster during the month and the rest of the cargo trips would be of the two night variety. The pax flights have their fair share of night flying and coming from SGN to NRT at stupid o'clock in the morning is not high on the list of fun but at least you don't have to stage through OKA. OKA is the biggest pain in the arm and THAT is the worst thing they did when they turned this from the best job around to another job.