How do I communicate between multiple threads?

I'm writing a plug-in for another program which uses the native program to open a series of files to extract some data from. One problem I am having is the process takes a long time and I want to keep the user interface from hanging. Plus I also want to give the user the ability to cancel the process before it completes. In the past I've used a background worker for this type of thing, but in this case I don't think a BackgroundWorker will work.

To create a plug-in through the API I am using one can create a custom command by inheriting from an IAPICommand interface. This interface includes an Execute(Application app) method. The class is then instantiated and the Execute() method is called by the program when the user evokes the custom command in the program.

The Execute() method is passed a reference to the current Application object when it is called, and it is this application object that is used to open the files to extract data from. However, the application instance is not able to open a document when requested by a thread other the the original Execute() thread.

So typically the UI would exist on the main thread, and the time consuming data extraction would be performed on a secondary thread. However, in this case the data extraction must be performed on the main thread, and I need to create a secondary thread for the UI.

Here's a stripped down version of the code.

class MyCommand:IAPICommand
{
    public void Execute(Application app) // method from IAPICommand
    {
        Thread threadTwo= new Thread(ShowFormMethod);
        threadTwo.Start();
    }

    public void ProcessWidget(Widget w, Application app)
    { 
        //uses an App to work some magic on C
        //app must be called from the original thread that called ExecuteCommand()
    }

    //method to open custom form on a seperatethread
    public void ShowFormMethod()
    {
      MyForm form = new MyForm();
      form.ShowDialog();  
    }
}