I need some help understanding overshoot and ringing in MOSFET half bridges
What I am having difficulty understanding are the reasons
  behind overshoot and ringing in V_DS.


The ringing is due to the parasitic capacitance of the MOSFET reacting with the inductor as an underdamped 2nd order system. This capacitance can be in the range of 100 pF to 1nF. Read the MOSFET data sheet - it looks like it will be about 900 pF.