Virtual Machine (VM) is configured with "bridged network" but cannot ping host (host cannot ping VM also) and at the same time both can ping IP addresses on Internet.

The problem is that you cannot ping to ↔ from host and guest. Other networking is fine.

Unchecke the DNE LightWeight Filter and it will fix it. 

  Network and sharing center
  Select your adapter that has Internet
  Click properties button from the Connection Status Window
  Uncheck DNE LightWeight Filter in the Adapter's properties
  Click OK and wait for your adapter to reset itsetf