It's broken.
You've got an interesting question, and I've tried to answer it in several different ways. My first try was to use the cost for "raw" mithral in GP/Lb and subtract from the cost of armor.
The cost for Mithral according to the DMG is 500GP/Lb. Seeing as how a Chain Shirt weighs 25 pounds, and mithral items weigh half as much, we should need 12.5 pounds of mithral for a chain shirt. That works out to:
12.5Lbs x 500GP/Lb = 6250GP total
But the mithral shirt is only supposed to retail for 1100 (Whether you use the "mithral shirt" entry from the DMG treasure tables or take a regular chain shirt and add the mithral cost to it). We have a problem.
Looking at the PHB entry for a chain shirt, we see that a chain shirt includes a layer of padding under it. Assume this padding is equivalant to padded armor and weighs 10 Lbs. Now there's only 15 Lbs of metal which needs to be mithral. Mithral weighs half as much as steel, so our price for materials now works out to:
7.5Lbs x 500GP/Lb = 3750GP total
Still way too much. If we go in reverse and assume that the 100 for a regular chain shirt will cover our materials costs for padding, straps, etc, and we charge the 500GP/Lb rate, the actual mithral part of the armor weighs only 2 Lbs (Actually a little less, as we havn't paid labor costs for a masterwork item yet). Which would mean the actual metal on a steel chain shirt would weigh 4 Lbs. I've never handled an actual chain shirt, but this seems way too light to me. Also a quick crosscheck with existing numbers shows that the steel in a regular chain shirt should weigh approximately 15 lbs (25Lbs - 10 Lbs (the padding)). So we're still way off.
There are two solutions. Both are completely unofficial interpretations and/or extrapolations based on other rules, but they're the best we can do.
1 - "Mithral" chain is actually made of a mithral alloy, and therefore costs less than the listed cost for "pure" mithral by the pound.
2 - The DMG on p243 states that items crafted from mithral are treated as masterwork in regards to crafting times. If you already have the material, then the cost to get the armor made shouldn't be any different than a masterwork suit of armor, as it will take the smith the same amount of labor to create. (This is barring other special cirumstances, such as special equipment required for crafting mithral armor)
I like Option 2 better, it seems cleaner to me. However, with that you're still stuck with a bad price for Mithral per pound. I thought about working backwards from option 2 to extrapolate the "correct" cost/Lb for mithral, but since the armor price is by Light/Medium/Heavy and the commodity price is by weight, it probably wouldn't come out right (not to mention complications like the padding mentioned above). If someone wants to try to work out some sort of average figure, I'd love to see the numbers.
Hope this helps!