The air gap was one of my first thoughts. This is common on woodframed homes, where you have the a vapour barrier, insulation / insulation + framework, a moisture barrier, an air gap and then the water shedding layer (siding, render carrier, brickwork etc). Even in the UK where wood framing is less common it's almost identical to our roof structure where you have insulation, the roof framework (with ventilation in the eves), a water barrier (classically tar paper) and then the water shedding layer (concrete, slate or clay tiles).
I guess one challenge is how you would have sufficient ventilation in the gap underground, perhaps you'd have to use some kind of forced air ventilation with all of the problems that would entail.
However, by the time you ventilate that space you have now negated any thermal mass advantages you had from building under ground in the first place by introducing ambient air.
Adding water channels as well were my thought. Just as air gaps allow moist air to exit wall cavities, external drain channels should prevent water from pooling and penetrating.
Presumably in an underground house, you'd want your roof to have a big air gap that could serve both purposes -- excess water removal and moist air exhaust. I believe many house foundations routinely add an external air+water drain/gap layer like this.
I guess one challenge is how you would have sufficient ventilation in the gap underground, perhaps you'd have to use some kind of forced air ventilation with all of the problems that would entail.
However, by the time you ventilate that space you have now negated any thermal mass advantages you had from building under ground in the first place by introducing ambient air.