If you are looking for a durable and permanent solution then I think you should go with something like Norm is suggesting.
However if you are looking for a lower cost and not so permanent solution there are a few ideas that I have used in the past. First of all you can create your graphic file and print it side by side on a piece of semi-gloss or matte photo paper. This is thicker than normal copy or printer paper and gives a better quality. But take note, when you cut this out leave the mid-line uncut. You will FOLD the id to be double sided. Trying to laminate two pieces of photo paper is not a wise move because it rarely works unless you have HUGE border of laminate around the edge.
If you want you can also use double sided
photo paper. I haven't used the Epson but right off the top of my head I can't remember the brand I used. I know they sell it at Camera Co-Op. But you will get a much better lamination with a single sheet.
As for laminating you can take them to Kinkos and let them do it or you can do it yourself. If you do it yourself be sure to send the pouches through the machine at least twice. If you have laminator save your self the time of cutting by using
these.
Well those are my tips. Hope something helps.
Prophet out.