I\'d like to have iOS to open URLs from my domain (e.g. http://martijnthe.nl) with my app whenever the app is installed on the phone, and with Mobile Safari in case it is no
You can't, as far as I know, make the entire OS understand an http:+domain URL. You can only register new schemes (I use x-darkslide: in my app). If the app is installed, Mobile Safari will launch the app correctly.
However, you would have to handle the case where the app isn't installed with a "Still here? Click this link to download the app from iTunes." in your web page.