I believe if you take the 2 surfaces and choose (in the Maya Surfaces mode) Edit NURBS > Align Surfaces > . Then choose Edit > Reset Settings in the window that pops up (this is because in this case I believe that the defaults will work well for you) and then hit the "Align Surfaces" button it should do the trick.
When I do as you say, I end up with a totally messed up result. I've tried to change the settings, and I see how the NURBS surfaces connect to each other, but they do not do it overall, only at the top or bottom.
Is there any other way to achieve the result I want?
I created the surfaces with 3 EP curves, then I rebuilded them and lofted them together.
You may have to rebuild the surfaces. This is fairly common for NURBS. You'll want to make sure that you have the same number of spans, and that they line up in both the U and V directions. You'll also want to make sure that all of the surfaces are going the same direction, or you'll get wonky attachments. There are several tools in the Edit NURBS menu (Rebuild Surfaces, Reverse Surface Direction (go into the options for each)) that may help in getting these surfaces to match up. Another thing you can try is some Stitching. There are three stitching tools within the Edit NURBS > Stitch menu that may also help you stitch the edges together. It's not the same as attaching them, but it will do basically the same job.
My other question for you is, does this need to be attached? Often times models are made up of separate pieces that never get attached. If there is a need to attach it, then sure, but more often than not you can get away with simply grouping several surfaces together to get one item and then hiding the seams with either a clever bit of texturing, or just putting the seams in logical and "no one will ever see it" places.
Without physically seeing or messing with the model, that's probably all the help I can give you on that.