It would count against both, but your home internet twice.
Using the Unite browser, traffic will flow across your wireless plan via RIM (in an encrypted tunnel) to your Unite server at home. The Unite server will make the web request and return the results back through the tunnel to the Blackberry.
The only reasons (IMHO) to use the Unite browser is to access pages in the home/office network that are not accessible from the outside, or to monitor/control the sites the Blackberry browses. If you only want the first case I would suggest the Unite Policy Mods thread to allow both the BIS and Unite browsers. This is how I set up mine, I can access private pages via the Unite Server, and the rest of the web through the BIS.
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