Due to the construction of my walls and the replacement windows I am unsure how to finish the inside trim to allow for 4 inch vertical blinds to work right. How much depth is needed for operation of these blinds?
The blinds should come with specs telling you the minimum depth to leave. Assuming that the blinds when full open are just about 4" from front to back, you’ll need something more than that. Usually when I see them it’s in commercial buildings and there will be a large ledge below and overhang above, lots more than the depth of the blinds in the full open position. A valence can be positioned at any depth greater than the minimum to cover the top of the blinds.
However, there is usually some minimal depth where the blinds will still work, but just be able to twist all the way open, and there may be difficulty fully drawing the blinds to the side.
Could you better explain your concerns? I hang these a lot but they are usually surface mounted above the opening.
WhiteSIFL: Sorry to be so late responding, too much happening here. My house has unusual walls, the original is 2bys with 3/8 plywood on each side. We stripped the siding, added insulating board and OSB to the outside. On most of the windows I trimmed them like a picture frame and hung horizontal mini-blinds within the frame. However for the living room we are wanting vertical blinds. I would have to build out the trim to allow mounting blinds “within” the frame, which has prompted the question. Perhaps the cleanest approach would be hanging them outside the frame as you suggested. Are there special brackets for this mounting? Thanks in advance!
Best to buy the pelmet that works as, or comes with, THE BRACKET to mount the blinds.. and logically the pelmet is there too making it look neat and blocking the glow that would egress up through the gap. OR buy blinds that come with pelmets - the pelmets that are the track for the blinds, and it may come with suitable bracket .. Make sure that you get the mounting brackets.
What I mean is, buy the blinds and the pelmet as a matching set.. Much easier than fussing with attaching the blinds track and then a pelmet over the top.
(bolding mine)
And yet another example of why I love the SDMB.
I’ve been a carpenter since before I graduated from high school and a General Contractor for over 20 years, and I can’t honestly say that I’ve ever even heard that term. Ignorance successfully fought, once again. 
Most vertical blinds will come with brackets that surface mount. They will also (or should) come with a valance that clips over top to hide the mechanisms and brackets. They are usually only adequate, style-wise. You might wish to add a trim or pelmet piece instead of the valance depending on the level of ‘finish’ you desire.
Mount a length of two by four and paint to compliment your room then mount blinds to that. That’ll give you an extra inch and a half.
Upon re-reading I think I better understand your concerns. I still stand by my suggestion of mounting them above the windows however it seems you could build out the ‘soffit’ or sash stop to accommodate the blind hardware and then add a valance or trim piece over that.
You could mount longer ones from the ceiling to leave a foot or more of space. Room to walk behind to slide open a door without having to brush them aside. Or room for a cat to lie in the Sun.