You dont say what car it is, buy never mind Drum or Disc. Sounds like they are rusting up, as the brakes were wet when you applied the hand brake, so the need a little shove and they become free.. This should not be much of a problem as once you have used your brakes a couple of times it should clear any rust on the Rotor.. a couple of helpful tips if this problem is persistant is to gently apply your brakes on very lightly on your last 1/4 mile home when its raining, to warm up the brakes slightly so they are dry when you apply the Handbrake, or leave the car in either 1st or Reverse gear and leave the handbrake off, reverse, if the car is facing downhill or 1st if its facing uphill..... If all this fails to help get a qualified mechanic to have a look at them for you.... Hope this helps.. Wilmot