Masonite fake stucco

 What you may have is a material that came out about 
       17 years ago and was an early form of synthetic stucco. 
       I have only seen this once and had someone write me 
       from North Carolina that had this on his house. 
       It was applied to the foil covered foam sheathing. 
       This material came in bags and was mixed with a 
       drill and applied to the foil sheathing. The house we worked 
       on was an owner built tudor style house in Alexandria. 
       We stuccoed a stair tower that was started years before 
       and never finished. We used lath and stucco, of course. 
       The then current owners showed me the leftover bags 
       with instructions on how to put it on foil-backed sheathing. 
       I required no lath. The owner put it on real rough and painted it white. 
       I don't remember who made this stuff and have only 
       heard of it twice. 
 

                    Masonite-another form of fake stucco

Another material you may have are the pre-made stucco boards 
       you referred to. These were used on a lot of tudor style houses 
       in the last 30 years. They are masonite(see attachment) and 
       I think they quit making them after the lawsuits over masonite siding. 
       MASONITE I copied this from Here
Masonite Hard Board - (Masonite) - did have a class action suit filed. The hard board siding was not used a great deal in the Pacific Northwest but you do find it from time to time. Most of the Masonite hard board siding came in panel form. On expensive 
homes you might find the Masonite "clad board". This is where Masonite covered the hard board siding with a "stucco" appearing material. This material was used on houses where people wanted to have a "tudor" looking home. If you have Masonite
 Hard Board siding you may call their claim line at
       1-800-330-2722. 

       Here is a picture of a piece we tore of a 15 year old house. 
       We pulled it off with our fingers. 

       Even if they still made this I doubt you would want this stuff on 
       your house, if you knew what it was. It has about the strength of 
       cardboard. Still, you may have it and probably can file a claim 
       with the manufacturer. 

       Ideally a tudor house should have a flashing over every 
       horizontal member. Most people elect not to do this 
       due to appearance. You honestly can only see 1/4" 
       of the flashing and usually these are so high off the ground 
       you can't even see them unless you really stare. 
       We are getting ready to stucco an addition to 
       match an existing house where the tudor boards were never 
       flashed. You can see where the paint is peeling and the boards 
       are probably rotting. I should insist that they be flashed first 
       to protect the stucco. 

       Assuming the house has real stucco: 
       These boards( the horizontal ones only) can be flashed 
       properly if you cut off part of the stucco over the 
       board a few inches to nail the flashing tight to the sheathing. 
       Then the stucco needs to be patched to overlap the sheathing. 
       If you go to this extreme, you may want to do the entire panels 
       so the patch doesn't show. 
       You can get pre-made flashing at Home Cheapo for about $2.50 
       A 10 foot length. 
       Yes, you should have caulking, but caulking shouldn't be relied 
       on 100% to keep the house from leaking. 
       Tyvek is a plastic vapor barrier applied to sheathing, like tar-paper. 
       I like tar-paper better. 

       If this is Masonite or the stuff applied over foil board you can 
       upgrade to real lath and stucco. Pittsburgh has a reputation for 
       good plasterers and I'm sure you can find someone in your area. 

       Hope this all makes sense.