To the best of my knowledge, glossy papers are one-sided - the reverse is unsuitable for any inkjet printing. Also, many coated inkjet papers are only coated one side.
The only thing is to use a double-sided inkjet coated paper (smooth matt finish) or thin card (say around 200gsm) but folding needs care to avoid "crinkling" along the fold line.
Why does it need to be glossy? A good quality coated inkjet paper will produce a good image reproduction. If you really must have glossy, spray after with a gloss-finish UV spray.
If (I assume) you are producing cards (Birthday, etc.?) then print your photo image on the glossy size (use a fairly light weight such as say 120gsm so can fold easily) then print your greeting on plain paper and attach that, after folding, inside with some double-sided adhesive tape along the "back" edge one side or a little adhesive - a few little drops work well. Hope it's clear that you insert the folded inside paper, open the outer so the inside paper lies to side behind the image, then glue lightly as described along the edge that will face the inside of the back. Fold back over and press along the join. Don't glue to ends (i.e. top and bottom) or that could squeeze out. Like most things, simple to demonstrate, hard to describe in words.
Case Paper has one of the largest inventories of coated paper in North America in both rolls and sheets. We have everything from commodity to premium grades in both text and cover weights in standard size sheets and rolls. With our state-of-the-art converting facilities and extensive inventories, we can customize sizes with fast turnaround.