You will face Jed after you give Katey the Zombrex shot. This will take place anywhere from 7:00 PM to 8:00 PM depending on when you give her the medicine. Preparing for this fight wouldn't be a bad idea. If you decide to go for some combo weapons, pick ones that are melee based and the helmet/beer combo for health. Though if you decide you don't want to waste time, a broadsword works very well too. The door to the roof is locked once you meet him. The snack area is open and you can just keep regaining health in that area if need be. Just go back and forth refilling your life and attacking him. He will not follow you back inside.