Then you need to apply a separate material to the transparent parts of the mesh and give them the transparent material in Unity and leave the rest of it as standard opaque diffuse. You'll still get sorting issues with the transparent bits, but they won't be quite as bad.
If you want it to be semi-transparent, you'll need to use a separate material for the parts that are to be that way. You're running into sorting issues. Otherwise, use the cutout rather than transparent shaders - i.e. Transparent/Cutout/Diffuse - that will use alpha test and it'll sort fine.