Everyone has fantasies, that's for sure. Healthy or not depends on whether they indulge them or act on them, or attempt to.

It sounds to me like he is consistently violating your boundaries regarding fidelity in your relationship. Everyone has different things that they view to be cheating. For some couples, it's not an issue unless there is actual intercourse. For others, even viewing porn can be an issue. Different strokes for different folks.

To that end, however, you are also violating his boundaries by searching his phone. Though you do this in his presence, and outside his presence, it is still a very clear statement on your part without uttering a word. It says plainly "I don't trust you."

If you continually search the phone, internet history, etc, you will absolutely drive yourself crazy. As PP's have said, on any given day, anyone's internet searches might seem odd... but, context dependent. I don't think "I -blanked- my little girl" could be searched in any context than what it states plainly. Knowing that, nevermind distrust... with two teenage daughters, you've stumbled on a potential danger.

From a personal point of view, my advice would be to take screen shot captures of that exact search and sit him down and talk to him. I would be asking some very tough questions. Such as "why" and "is this an issue that needs to be addressed". Because the hard hitting reality here is that, if he IS in fact having these urges, and he does attempt to act on them, what happens? Two teenage girls could come away with some very serious trust issues and that's at a minimum, depending on what could or does happen. After talking to him, if I wasn't satisfied with his answers, I would start making plans to leave.