Can I use aluminum or plastic sheeting between decking and joists to waterproof under a deck?
Site-built deck drainage

Here is an article in Fine-homebuilding on site-built deck drainage.



In this article they use EPDM rubber roofing material.

I wouldn't hesitate to use this or creative alternatives, but I wouldn't consider this as a "waterproof/roof" system. I would consider it rain-proof where it diverts rain and rain-runoff from underneath the deck.

Retail deck drainage

There are products available that are designed for this as well. Like Timbertech Dryspace for example.



My opinion

Using either a site-built or retail product, I still wouldn't store anything under there that would be ruined from getting a little bit of moisture now and then.

If you want a real waterproof roof, then build it as a code-approved roof with code-approved materials installed how they were intended to be installed.

Issues

One potential issue I can think of right off the bat is that dirt and debris will collect in there, so do you have a plan on cleaning this out? You will need access from time to time to at least stick a hose at the highest part to rinse it out.

Another potential issue is that this would limit the airflow and potentially increase the humidity between the decking and drainage material. This could contribute to things like cupping or premature finish failure on wood decking.

Real Roof (info as requested in comments)

60mil vinyl can be considered an approved roofing surface. You would use something like this if you are not putting another surface over the deck.



Another roofing option (if you wanted to add wood planks) would be to do flat roof (i prefer a torch-down roof): then build panels out of your deck surface, or attach the decking to sleepers (see image below), or use wood tiles