layering high dielectric constant and high dielectric strength materials in a capacitor
These material properties are tradeoffs and cannot be improved by alternating materials.  Each one becomes the weakest link.  

Barium titanate k=1200, E = 1.2 kv/mm (max)  k*E=1440
Mica            k=3   , E = 118 kv/mm (max)  k*E=354


multiplying by cost gives you another metric kE$ /mm

When you compare every material, you find that plastic is most economical for some such as polycarbonate, polystyrene  unless there is some other requirement such as mechanical strength, thermal resistance or max temp size, etc.

For example Teflon tape and epoxy coated paper are common HiV materials used inside power transformers and also mineral and/or vegetable oil purified for transformer quality voltage insulation 25 to 75kV/mm with high thermal conductance.

The purity of materials ( and processing) also affects the max. electric field E.

If C1 =1 and C2=100*C1 are in series the net C value is \$C= \frac{1}{\frac{1}{C1}+\frac{1}{C2}}\$  Which ends up being pretty close to the smaller Cap C1 or 0.99.

Similarly, if two materials with vastly different E field limits are in series, the weakest link will breakdown.
Bottom line is there is no advantage to interleaving these two materials unless there are some other requirements not given.