I tried different kinds of underwear with little success, and I'm trimmer than you.
I suggest you surrender to the fact that underwear meant for normal activities are not suited for cycling.
compression shorts don't have padding but give the support and stretch needed for cycling.
The key to look for IMHO is "flat seam" I never tried these but they seem to fit the bill.
http://www.amazon.com/Compression-Shorts-Running-Cycling-Basketball/dp/B00FJ1IV7E/ref=sr_1_1?ie=UTF8&qid=1451914100&sr=8-1&keywords=mens+compression+shorts+flat+seam
when like you I was only riding 5 miles or so, I really didn't want to go with padded cycling shorts, but I was so uncomfortable I just bit the bullet and bought a pair of these
Amazon.com: Baleaf Men's 3D Padded Bicycle Cycling Colored Underwear Shorts: Sports & Outdoors They are not heavily padded and are short like boxers so I wear them under regular loose fitting shorts/pants when I'm riding my bike to an event. They are inexpensive but surprisingly well made. I still use them.
Good luck to you. Oh and to share my experience, when I went with cycling shorts, my comfort level increased to the point that I was riding longer and farther.
Happy Trails to you.