It isn't how many walls it has. A strong wheel is strong and doesn't know what kind of bike it is on. Steel rims are definitely heavy and not all that strong, you can certainly beat them with a good wheel these days. You need good tires under a lot of pressure (relatively) on a tandem. Figure each wheel is probably supporting 200 lbs or more. It is pot-holes and such that do the damage.
I don't know how much you want to spend here, but you can easily equal your bikes cost on new wheels. If you don't want to do that, you might have problems getting something worth having.