The right way to do this is to rabbet the stiles and rails, put the screening in the rabbet, staple it in place and then the moulding on top of the stapled screening. This all is on the exterior of most if not all commercially available screen doors.

Thanks for the response Millworkman. Problem is I have very limited skills and equipment. Can't do a rabbet, don't have a router. The doors are only my 3rd build ever. Ambitious on my part but nothing ventured, nothing gained. The door just has vertical and horizontal cross pieces on the bottom. Want to add some trim to the interior edges to make it look more professional. As usual, it seems sometimes the more simple things hold me up. I'm trying to wing it, so I'm greatful to hear from people that know what they are doing.

Since you have no skills in building your doors, you can create your door the way you want. It's just that the profile should be face out so that you can get more air from the porch.