When it comes to creative website design, there is actually a very long planning process. You have to mockup a framework, come up with a color theme, the layout, and finally graphics to support everything. All of this work has to be taken in consideration before you even get to coding out the site in HTML and CSS.
As with anything creative project, it takes time. If you aren't a creative person you might expect someone creative to be able to crank out a creative project in a short amount of time. But it usually doesn't work that way. Creative people aren't creative 24/7. And so you have a "creative" time that is spent planning, organizing, getting inspiration from other sources. Brainstorming concepts and ideas, and then seeing how they might translate to real world applications. And sometimes the concept doesn't translate well into what you original expected, so you have to back step or modify the original plan. Maybe even go back to steps of coming up with a completely new concept.
When it comes to the web design, it is a two part process. You have to design everything first, then code everything out. Usually the initial design is done in Photoshop as a simulation of what the website will look like when coded out. Then once you finally get a site the way you or the client wants it to look and the feel of the website, then you move into the process of translating that design into a website, or the coding aspect. So in a sense it actually a long process of design and a short process of coding. Of course if you are working in some functionality into your website then that will take more time on the programming end, also known as the "back end".
Of course one constraint of this whole creative process is budget. If the project you are working on doesn't allow for the time and effort it takes to have this creative flexibility and space to really do it right, then the end project usually suffers as a result. Of course you still pull off a decent website, but it might not be at full potential.
And so if your company is truly looking to stand out and have something creative, it should be known that is will take time and does cost a little extra than you standard programmer working in his basement.