I seriously doubt that was done as a three colour print. The easiest way to do it, which is how I imagine they did do it, would just be to use transparent waterbased inks. Two colours, what you see is what you get. Easiest thing in the world.
As for how to design it... here's one possible method (but there are many). Create your text, you can do each word separately, then copy and paste one over the other to check that it looks how you want it to. Set the opacity level on the layer to create the merging effect. But there's no reason you can't work on them completely separately until you have things how you want it.
Once they line up to your satisfaction, either submit that file as is and the printer can separate and print, or you could even just submit that as a proof of how you want the print, and give them the original separate text files so they don't have to separate something that's already been done.
