I've never used Hyper-V, but I run Virtualbox and the solution seems to be the same. http://technet.microsoft.com/en-us/library/dd560637.aspx describes the "snapshot" functionality, which is just the "differencing disk" you're looking for. However, (in Virtualbox anyway) you can't edit the parent hard drive and have the snapshot offspring work correctly, to my knowledge.
Taking a checkpoint/ snapshot of a VM is like using a parent disk -
all the changes to a VM after a snapshot is taken are written to a new
VHD (You’ll see this on your physical disks with a .AVHD extension
where you specified to save your snaphots). If I create a subsequent
snapshot then another AVHD is created and changes are then written to
this newer AVHD file.
As I thought, Hyper-V works exactly like my VirtualBox snapshots, it freezes the source virtual drive and writes all changes to a separate "differencing" file. You can't edit the parent at all once you've made a snapshot, unfortunately (the snapshot will break).