How do I model a structural interface that is not continuous in the out of plane direction?

In general, it may be better to adjust the strength of the reinforcement, but not the stiffness, depending on the spacing.  This is because, in general, the stiffness is not reliably known.  A starting point could be to set a value of stiffness an order of magnitude higher than the modulus of the material for the normal direction and the same as the modulus for the shear.  Likely, the results are more sensitive to the strength of the liner and the interface versus the stiffness.  A sensitivity analysis should be performed on the stiffness.