It's tough. One of the toughest parts about programming ANYTHING is when customers have preconceived notions of what it should do/look like. In projects when you get the job description before the actual visual design you might have a chance by giving them a list of requirements, but once they spend two hours making a granite sculpture of their website design it gets a lot harder to change their minds.
If you haven't been given the design yet, you might want to make it a requirement that at the very least you and their designer come up with a design collaboratively. If you get in touch with them directly it might be easier to explain your demands and critique their work from a web scripting perspective without creating a lot of back and forth through a third party. It also might help to keep a running list of things you can't do - every time a designer gives you an infeasible project, make a quick note of why it can't be done and pass that on to other clients in the future.
There are also plenty of books and articles on usability and good web design out there for you to reference if you need to prove to them that it's a different world and that they may not have the best frame of reference for it. If you're really dedicated, there are plenty of web design courses out there that could give you the credibility to take full charge of the design yourself.
No matter what you're thinking, know that the solution is definitely going to require a large amount of collaboration between you and their print designer. Whether it's to the extent of you coming up with a template for the site and him filling it in with illustrations/logos or the two of you spending some time on a chalkboard somewhere plotting out the layout, you're going to have to come up with a situation where both you and your client have a significant amount of say in the final product.