On most projects I've been one, designers has produced HTML code, then developers turned it into ASP.NET, including master-pages etc that should really be a part of design.
After it has become ASP.NET, designers could not work on the code with their tools.
I know that a lot of the design of ASP.NET is made with the purpose of separating code and design, and in principle designers should be able to work on design aspects with the Visual Web Developer, but I've never seen a designer using VWD.
How is cooperation done in practice, and what is about the best one can expect from a designer?
A good ASP.NET developer will intelligently use the set of controls available. For example, in most cases, the ListView will do everything the GridView can, and produce clean, SEO-friendly markup.
In the ASP.NET environment, I would encourage the use of Expression by designers. Business owners can avail of the new deal from Microsoft and obtain VS, Expression, etc., for $100 for three years.
I think both developers and designers have to embrace each others world for anything to work.