Yeah, you need the source part and the target part open in separate windows.
What helps is to resize the source part so that it is about half as tall and half as wide as normal, and then move that source part window so that it's located in the lower left corner of your screen.
Change back to the target part (make sure the window is activated), and then execute the command (Feature > Copy > New Refs > From Dif Model > Independent yadda yadda yadda). Follow the prompts in the message area (I'm assuming you're in 2001), and you'll be able to click on the source model in the smaller window and select your features you want to copy.
Keeping the smaller window open also helps when you're trying to figure out functionally equivalent references for placing the features you're copying.