The International Energy Code for Conservation (IECC) calls for a continuous layer of insulation somewhere in the wall assembly. They instituted this requirement to circumvent the thermal bridging factor of the studs which wick away 40% to 60% of the R-value of batt insulation installed between studs. If you want to introduce a layer of continuous rigid insulation in an adhered stone veneer wall, we recommend that you install this insulation on the inside face of the studs, just behind the interior sheathing.
If you insist on installing rigid insulation on the outside face of the studs, you need to realize that the rigid insulation is actually not all that rigid. Point loads from errant baseballs or ladders leaned against the wall can dent the rigid insulation and crack the veneer. To prevent this damage you will need to install a thick layer of cementitious materials over the insulation to provide a stiff, stable substrate upon which to mount the stone veneer. Elsewhere in this Guide we tell you that the cementitious layer behind the stone (scratch coat + mortar bed) should be 3/4″ to 1-1/4″ thick. If you are using rigid insulation behind the stone, we recommend that you aim for the 1-1/4″ thick layer.
Walls with rigid insulation installed under the stone veneer should NOT have the stone veneer touch the ground. While the stone is tough enough to survive this exposure, the rigid insulation, the expanded metal lath and the flashing should not touch the ground or be buried below the sidewalk.