I have an usb wifi board without drivers for Mac OS X ML. Sometimes I have to connect to internet using the external board and need to pass the Ubuntu internet connection running on VMware Fusion to my Mac. Is it possible? Thanks.
Yes, you need to used a "Bridged" connection in your virtual network adapter using auto-detect.
Fusion has three virtual networks: Bridged (which usually be auto-detect of your physical network connection), Host-Only (which gives access between the host and the guest only), and NAT (which will be a different subnet than your host machine and will give access to the host and the internet connection).
The issue maybe that your Bridged connection is not set to auto-detect (most likely it is bound to your physical network adapter)
Your Ubuntu machine should then use the NAT to get access to both your Mac and the Internet.
ie. your Mac might be on Network 192.168.1.x/24 and your Ubuntu machine would be on Network 192.168.2.x/24 and the virtual machine configured to use the NAT.