A suggestion (not a definitive answer). I'd model the assembly as a 3x-layered construction:

• layer1: matA (150mm?), 'exposed area'-weighted composite of ~20% wood + ~80% stone/rubble
• layer2: matB (300mm?), ~100% stone/rubble
• layer3: matA (150mm?)

Material properties (a first rough guess):

• wood (sal? cedar?)... k: 0.1 W/(m.K), Cp: 1500 J/(kg.K), rho: 500 kg/m3
• stone/rubble (?) ... k: 2.0 W/(m.K), Cp: 1000 J/(kg.K), rho: 2000 kg/m3

... matA ('exposed area'-weighted composite): matA: k: 1.6 W/(m.K), Cp: 1100 J/(kg.K), rho: 1700 kg/m3

That's Thats's the easy part. Tougher questions include wind exposure, air tightness, etc.