As said, 1 ply is the norm and most passenger car tires have this. I don't know about truck tires though.
Usually only high performance tires have more than one ply (two usually) to increase sidewall stiffness and improve steering response. Materials vary, like polyester, nylon, rayon, steel, etc. depending on how much strength is needed.
Blowouts usually have nothing to do with sidewall construction as far as I know, although if you run your tires underinflated/overloaded it increases the chance of this greatly because of stresses like heat.
What tire model are your wife's BFGs anyway (out of curiosity)?