I would suggest looking at ASTM standards D471 (Effect of Liquids ...) and D543 (Chemical Combatibility... ) as a starting point. Their coordinates are shown below
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GC-MS seems to work for your purpose. Take that membrane and attach it to a e.g. gas-tight bottle, add the solvent on top and give the gas sample to GC-MS, then you'll know if the membrane is transparent for that component.
Maybe there are more advanced apparatures available for that.
I know some time passed since you asked the question, but by accident I found an apparature which could be of great interest for your problem. The thing is called "franz diffusion cell" and is frequently used to test diffusability of chemicals through the skin, you may use your membrane for this! I also attached a link FYI.
maybe you already solved your problems, but again I found an instrumentation which would fit perfectly to your needs. Kinesis (German company) offers a great variability of Franz Cells - manual or automated measurements. See the link attached.