uniting,
If you mean that you wish to apply a Stroke outside the whole thing (only), you may:
1) Select both unstroked paths and Group them;
2) In the Apperance palette flyout click Add New Stroke, set its properties, and drag it down beneath contents in the Apperance palette.
With this, only the part of the stroke outside the fill will be visible, as is the case for a normal path with the Stroke set to Align Stroke to Outside.
You may double the Stroke Weight, or Align Stroke to Outside.