Are your basement walls really only 4" thick? I find that hard to believe--my impression was that 8" is typically the minimum.

Chances are there's still a good portion of the concrete wall that's above ground and not insulated. Were I in your position, I'd go with a thinner layer of XPS (probably 1") on the inside of the concrete, then fiberglass between the studs.

The recommended level of insulation depends on your climate. In the Lower 48 above the Mason Dixon Line, R-20 is the recommendation of Building Science Corp.'s Dr. Lstiburek. One inch of XPS = R5. So you've got a ways to go. In a cold climate, one-inch of XPS on the interior is sufficient; I'm not sure if one inch to the exterior will keep the interior walls above the dew point, thus protecting the fg from dampness.

In a cold climate, one-inch of XPS on the interior is sufficient

Sufficient, that is, to keep the wall warm enough to prevent condensation. However, it must be supplemented by further insulation to achieve energy savings.

Thanks for the followup. Is there a way to test the wall to see if it is warm enough already--something like the floor test where you tape a square of plastic down?

Not that I know of.

But my thought is that the external insulation is so minimal--BSC and Building America recommend a minimum of 2"XPS for high performance in a cold climate--that the wall might still be cool. Plus there's likely extensive thermal bridging at the top and wicking up of moisture through the walls (unless there is insulation under the wall or a thermal break). If it were my home, I'd add at least an inch of high-R foam on the interior as well.

And don't forget the rim joist area, either with foam board well sealed, or easier and surer, spray foam.

Spray-foaming the rim joist area is an essential step in
creating a healthy energy-efficient basement.

Here is a link that might be useful: High R Value Foundation Assemblies