I compiled my module css files into separate SWF files and loaded them at startup, but still it seems you cannot have two class styles with the same name, as the first to be loaded into the application (in the other module) is what is used for the two modules. That seems really strange, because you need to keep track of all your style names, and may need to do major rework if a new module style names are the same as existing style names. If you did not have complete control over the style names, that could be a big problem.
Are you using Flex 3 or Flex 4?
In Flex 3 I can see where you would run into problems because there is just a single style manager to handle all of the styles. In Flex 4 each application and module has its own style manager so your different definitions of .searchHBStyle should work just fine.
That's good to know. Thanks very much.