S-parameter measurement of thin polymer film
The most precise way to measure the plastic material properties is to remove all the aluminum and measure the plastic with a split cylinder resonator such as the 85072A 10-GHz Split Cylinder Resonator. (Full disclosure: I work for the company that makes this particular resonator, but I am not speaking for them here.)

The split cylinder measures the dielectric constant and loss of the plastic at many spot microwave frequencies. This is much more accurate than measuring with the aluminum.

To measure with the aluminum coating, it will be important to take into account the effect of the conductivity and roughness of the aluminum. If the aluminum is pure and smooth, the material properties of aluminum can be taken from the values at Matweb. If the plastic is porous, and the aluminum coating process puts aluminum into the pores, in a close-up cross-section analysis it looks like the aluminum has teeth. This type of roughness will cause errors. Cross section analysis is shown in this video.

When using the aluminum coating, I recommend etching a Beatty Structure, which is described in "Analysis of Test Coupon Structures for the Extraction of High Frequency PCB Material
Properties". To improve the accuracy of the etching process, take advantage of the low-cost stencils available from OSH Stencils or elsewhere.

To connect to the ends of the Beatty Structure, attach the SMA connectors with conductive epoxy. The discontinuity at the connectors will be calibrated out as part of measurement process using the Network Analyzer.