Is it common not to have wood under the stucco on walls on a new home ?? my builder has left 4 or 5 4 x8 sections with no wood under the stucco and says this is very common to just wire lathe and stucco over the insulation?
Original three coat stucco used a 17-ga or 18-ga wire in a hexagonal mesh similar to chicken wire. Over-lapping horizontal layers of black tar paper would be attached to the studs or to sheathing and the wire mesh fastened to the studs and sheathing through the tar paper.
A house now under construction in my neighborhood was entirely sheathed in green ZIP OSB. Part of the exterior is stucco. The installers put black felt over the ZIP board and then nailed a metal mesh different from the original type over that. I assume they nailed into the studs and in between. I saw them apply the first coat. I don't know how many coats are used in this application, but I suspect it is only two.
I agree with DanDavis, the short-cutting garbage that you have is a typical scumbag-builder glossing over his/her laziness and unfounded cheapness to get materials to the project...I wouldn't buy even a candy bar from that lying filth.
What is VERY COMMON is "shut up sir, you don't know crap...just keep the money handy you stupid prey". Well, thank you John F for speaking up and not standing for being screwed! But now, you've created a job for yourself. You must go over EVERYTHING with the Inspector, whether that's a Town Inspector or Separate Hire (much more preferred, if affordable).
If this is something noticeable before, during or after completion I'd look into a warranty claim or a violation claim now. Get the Building Inspector involved ASAP.
Your concern is valid for at least 2 reasons. FIRST IS, that the structure is not complete and therefore not To-Code and has been weakened in a possibly crucial layer or area. SECOND IS, that the Code-Required air-sealing and vapor barrier is breached.
Air-sealing and vapor barrier aren't so important if spray foam is being applied after the stucco...which it's not. But, if any other insulation is going-in, then your violation is a future thermal chimney and mold breeding farm.