The iPhone has a great feature which lets web apps live side-by-side with native apps on the launcher. The user just has to visit the site once in their Safari browser and click the "Add to Homescreen" button. There are even some slick bubble popup frameworks that point the user to the right place:
However, once in fullscreen mode anchor tag links between screens might force the user in to Safari mode. To prevent this, do the page change in javascript, like so:
location.href = '../Home/';
This even works for links that go to a different domain, for instance if you are doing an OAuth to the facebook mobile login screen.