InDesign is primarily used for magazine/brochure production. Indeed, it's one of the industry standards in this respect, much like Photoshop is the industry standard for web design and texturing. Its direct and only real competitor is Quark. I'd say it has absolutely no relevance to web design at all.
If you're planning on going into web design, you'll really need to be able to write the HTML and CSS yourself. This is pretty much an industry standard skill now, and in fact employers will often want to see proficiency in Javascript and the ability to work around languages such as ASP.NET and PHP too. The convenience of Dreamweaver is nice, but for complex design it's not really very good (browser bugs will get ya).
The best way to learn to write HTML and CSS is to force yourself to use a text editor (even if it's a fancy one) and avoid the visual editors like Dreamweaver, which sacrifice control for ease of use — kind of like using an automatic seamless texture generator instead of editing it yourself. It's actually not very hard, but it can seem daunting at first. I've essentially taught someone to write good XHTML and CSS in a matter of weeks so it's not going to take years.
It's not clear what exactly you're doing at university, but as someone who's been a full-time web designer for two years I can say you don't really need much beyond Photoshop and Flash to do the job well. Dreamweaver is an excellent visual HTML editor, but practically all professional web companies have their (X)HTML written by hand nowadays. I do use Dreamweaver, but I only use the 'Code' part of it.