I've had to do this kind of thing before, to do it properly it does require configuration at the apache level. Look up these configuration directives...
Basically in their host or virualhost you would have to get the sysadmins to add
ProxyPass /myhome/ http://www.mydomain.net/
If your site uses internal redirects they you might also need to set up
So that they get redirected to the corresponding page on the .edu which will in turn get the right page from your site.
This requires the apache mod_proxy but any large installation will probably have that already (it might even be on by default i can't recall)
The way that this would work is your visitor would visit your page on the university domain, the university web server would then contact your webserver to get the page and then return it back to the original viewer exactly as though it had come from the uni server. does that make sense?
It does mean that in all the logs of your website on your server you will see many requests from the same ip (the ip of the uni server), even though these are probably lots of different people from all over the place.
One final point is that your university sysadmins might have an issue with this as it would in theory mean that you could publish any content that would then appear to come from the universities website and perhaps affect its reputation, then again because they are at least letting you put static content up already this might not be so much of an issue.
Infact, you might not even need to ask them, I'm not sure but you might be able to set this up using a .htaccess file.
I sincerely hope this helps you, let me know if you get stuck.