Hey all, I was dealing with this same issue and as it turns out, I was being too smart for my own good.
When I created the new project, I had not created the New Website, option, I had simply said new project. The same project type exists there and it even compiles and runs a web page, so it hadn't occurred to me that there was any issue.
Of course, I wasn't seeing the app_code folder either. Well, at some point, a little light bulb went off and I decided to start the project specifically as a web site. Now I see the app_code folder option and I assume it will work, although I haven't actually tried it out yet.