Hilltopfamily,
I just booked my family on the Explorer, which is the same layout as the Mariner, for Presidents week in 05. This is a school holiday for many in the Northeast, so the rates are higher that week.
We booked two connecting cat. H cabins for our family of 5 and the price was approx. $4100. These are outside cabins, on deck 3.
The one drawback of RCCL is that there are not many connecting cabins, and many of the cabins do not sleep more than 2.
We thought about a balcony and an inside across the hall, but my youngest will only be 7 when we sail, and I was afraid he would be scared or wander off!
RCCL does have a family stateroom that sleeps 6 I believe, but there are only a few on each ship, they don't have a balcony, and they are much more expensive than booking two cabins.
I guess my point to all this is, if you want connecting cabins, book early, especially during peak family times i.e. school holidays and summer!