You may have to tap on the URL to see it though. The URL field often hides the http(s)//: prefix when the field is not selected.
Besides the https:// indicator, you will also see a small green lock symbol on the tab of a secure page, when it is selected. I was making sure the lock still appeared, and where, when I noticed the URL thing.
All of this presumes you are using Safari. You'll have to double check any third party browser, though this is pretty much a standard, so they should show both too (though not always in the same place or by the same method).