My project is split up into a typical 3 layer structure for a Silverlight app. That is:
Sixto's answer is correct. With WCF you can share the BO DLL between the client and the service and re-use those objects (just configure the WCF service reference this way), but this won't work in your case. The issue is that your BO project is a standard .NET project and not a silverlight project.
Typically I structure my projects a little differently than yours:
If you moved your business logic out to its project and just referenced your common "dumb" objects, then you could probably create two logic projects, one silverlight and one standard, and just have the actual files in one and create links to those files in the other. That way you would get the same logic across both projects and it would exist in both Silverlight and standard .NET.