Are there any NEC restrictions for wiring 220v and 110v sockets on the same dual pole breaker?
Use a two-pole, common-trip breaker and you're set

Since you're dealing with a 20A circuit (where 15 and 20A receptacles are allowed), you can set up this mix of receptacles provided you handle it as for any other combination 120/240V load: all four wires need to be there, as shown in your drawing, and the breaker that protects it needs to be a two-pole, common trip unit (no handle ties here!).  This is written into the Code, albeit somewhat awkwardly, as 210.4(C) exception 2:


  (C) Line-to-Neutral Loads. Multiwire branch circuits
  shall supply only line-to-neutral loads.
  
  Exception No.1: A multiwire branch circuit that supplies
  only one utilization equipment.
  
  Exception No.2: Where all ungrounded conductors of the
  multiwire branch circuit are opened simultaneously by the
  branch-circuit overcurrent device.