You can create a utility project (configuration type: Utility in the project property pages) that has a post build event. You then call the batch file from that Post-Build event. If I remember correctly, utility configuration appeared in VS2005. But I believe the same can be achieved with another type of configuration on VC6.
Here is an example of a setup (this is the text of the Command Line property of the Post-Build Event):
set solutionDir=$(SolutionDir)
set platformName=$(PlatformName)
set configurationName=$(ConfigurationName)
call $(SolutionDir)PostBuild.bat
As you can see, you have all the flexibility of customizing the batch environment based on VisualStudio macros.
If you want to have this batch file called every time you build, add a dependency to the requiring project (your main executable or dll project for example). You can add your batch file to the solution items for convenient access (right-click on the solution and select Add -> Existing Item...).
You can even invoke the build command on this utility project to force the execution of the batch file.
At work we have a similar setup to start our unit tests each time a build is triggered.