Internal thread- mill hole to minor diameter, thread mill to major diameter
External thread- mill boss to major diameter, thread mill to minor diameter
So I feel like the problem is coming in because you have a cylinder or cylindrical hole in CAD, and it can't simultaneously be at the major and minor diameter. So either the milling or the threadmilling path will need to be offset. Or both, but one will be offset far more than the other.
I thought you said both are modeled to the nominal 2.375" diameter. But if that's not the setup, then what I write below won't be quite right.
Internal thread, you need to cut the minor diameter significantly smaller than that (closer to 2.3-2.31), and use a small PDO on the threads to get it to gage right, .020 minimum by my calculation for a pointy tool. And that's effectively zero clearance. I think you will want .030 to .040. So to check clearance, 2.375+.04-2.31=.105. This is less than .388-.25=.138, so it won't rub.
External thread, you would mill to a bit below nominal (maybe about .01 below) and use a rather large PDO to get the threads to depth. I would probably model the boss at 2.365 and drive both milling and thread milling off of that. You want the threads to cut to about .126 below your major diameter and would use this for PDO. As you can see, .126 is getting near .138. Here, a PDO of .138 is when things will rub.
The Harvey tool comes to a point. I think this is why there is slight disagreement between my numbers and Saunder's numbers, plus I think you want more clearance than a "2B" thread. I agree that the "tooth height" would seemingly make more sense to be 1/2 of .138, but I want to emphasize this isn't evidence of a math error or clearance problem, just some disagreement over terminology. PDO is a diameter offset and trouble arises when you run out of diameter offset between tooth and shank. If PDO is .100, the tool cuts .05 more radially.