You can't type it directly. But you can easily (with sufficiently recent versions of iOS), set up a shortcut to type it, which works quite well. Find an interrobang character somewhere, like perhaps this one: ‽
Then email it to yourself so you can load the email on your iPhone, or pull it up in Safari, or somehow pull it up on your iPhone, and copy it into the copy/paste buffer.
Then go to Settings -> General -> Keyboard, and under the 'Shortcuts' section, select 'Add New Shortcut'. Paste your interrobang into the Phrase field, and put an appropriate shortcut in the shortcut field. I set two up. One with '!?' as the shortcut, and one with '?!' (no quotes). That way I don't have to remember which order it is and they both work.
Voila!