Long ago, Backpacker mag tested bags with reflective liners and concluded that the reflective material must go next to the inner to have any effect.
This may be, as Pilate says, because putting it next to the outer will trap perspiration vapor in the insulation. That also means that by putting it next to the inner, you would be opting for a vapor barrier bag liner, loved by Warmlite fans, but hated by others. Warmer, but steamy.
Or it may be, as BP found, that the liners, even when perforated to pass moisture, don't work unless next to the inner. I'm not even sure they work at all - they were in vogue only for a short time (Yakworks Yaksac), then dropped by most manufacturers.
You can have a breathable reflective liner just by perforating it. Since you wouldn't want to perforate your inner, though, you'd have to add the weight of the liner, not worth it IMO. Would rather add more insulaton, instead. The lightest flexible (non-crackly) reflective material I've seen is the polyethylene-like Heat Sheets, that could be perforated with a meat tenderizer or whatever. The Heat Sheets is around 1 oz/sq/yd. You can get some pretty good additional R value out of Down, PrimaLoft or LiteLoft for an extra 1 oz/sq/yd.
Or you could look into reflective fabric that is vapor permeable. Be careful.
For example, Insultex claimed at one point that it would pass vapor one way (?), but now seems to have given up that claim. But a vapor permeable reflective coating is theoretically possible, so maybe you can find some out there. But looking for only 20-30 denier fabric with it would make it that much harder to find. Although Warmlite sells their fabrics, I'm pretty sure their reflective material is vapor proof, as they use it on VBL bags.
Best of luck.