You can line up all three sights; peep, rear sight , and front. It does lend a can't miss locked on feeling at times but it also defeats one of the key advantages of the peep and that is greater field of view. Of the guns I have that offer this, it is sometimes useful just to check that all is lined up right. It's a good way to instantly see if something has been bumped off.
George Hoenig does offer a nifty folding peep but not a folding rear. With him it's either open rear or peep not both.

Have both approaches on separate rifles.
My (only) bolt in .375 H&H was made with EAW hardware, including the drop into the back element peep sight. The rifle also has a fold-down open back sight that uses just the blade of an NECG-bought back sight, having milled off the standing part. Worked OK.

A .303 double has a JJ Perodeau-made peep on a replacement screw for the top lever. It works by aligning the wide vee and the front bead through the peep. It's very accurate in the way that Tanker describes, but also enables me to use just the wide vee back sight for most, relatively close shots with the double.

Regards

Looking through the peep's small aperture is the same as stopping a camera lens down to a small aperture...it vastly increases depth of field. I vaguely recall reading somewhere that this was one of the original intents of peep sights. The difference is very apparent, especially with a small aperture, i.e. not a "ghost ring" but something closer to a pin-hole. Not too fast or useful for hunting or low-light shooting, but being able to see front and rear sights both in sharp focus is certainly a nice change.

As far as both sights (peep and express) being lined up perfectly, how else could they possibly be? If they both are sighted at the same distance, and since they are both being aligned with the same front sight, they pretty much have to be in line with one another. If they're not they will cause there to be two separate points of impact on the target. If both sights are fold-down types, it would be more useful to sight-in the express sight at closer ranges, and then keep the aperture sight in reserve after sighting it for a longer distance. I have a couple of Sako bolt guns set up like that. A scope for primary use in QD rings, back-up irons on the barrel, and a nice little Sako aperture in my pocket to pop on top of the receiver in the field if desired or needed. Sort of a "two belts plus a set of suspenders" type of thing!

This sight, (made by SROSE) looks ROCK SOLID and
ready to battle D/G time and time again!!!

DR Hunter: This is the sight made by "srose" mentioned earlier. It does look good. It would work well for late models and those older pieces already altered. It looks like it could possibly be made adjustable for my light guns. I'm open to any and all ideas. Thanks.

Rick Stickley built me a peep sight for one of my doubles..It was a ghost ring peep, the base dovetailed lengthwise into the rib at the chamber area and was held by a spring and ball retainer..It was very dainty but strong as hell. It had no adjustment but was dead on at 50 yards with my designated load and for that matter with most loads. I could take it out and replace it with a solid base and you could not tell it was there. Later on I saw another much like mine but you simple took it out and turned it over and slide it back in and it didn't show..Rick is a genious with metal.