You could go from Haneda to Narita directly by bus
http://www.limousinebus.co.jp/en/tim...r_tokyu_h.html
The website says 75 minutes.
I assume from your post that you won't want to do this. My own guesstimate would get you to the city for 8am (perhaps a little earlier) and need you to leave Tokyo at 1:30pm for you to be at NRT for 3pm. About 5.5 hours.
You can plan a route and timetable using
http://www.hyperdia.com/ (select English). There are several train routes between Haneda Airport and Narita Aiport ranging in price and time. You can get from HND to central Tokyo in 20-30 minutes (longer depending on where you go), expect the journey to NRT from central Tokyo to NRT to take at least 1.5 hours.