composite wall stud

I wonder if anyone has tried this before. I came up with the idea to use a built up wall stud using 1" inner hardwood-3/4"foam-2" outer softwood. I'll attach a couple of views. The cavities between the outer and inner layers of wood are for sliding in pieces of plaster board. My concern would be how to fasten the outer and inner layers of wood so they more or less act as a unit, I imagine screwing through the softwood and into the hardwood might work.