The examples provided above from the IRS regs talks about the roof membrane, which is not the major component of the roof, so replacing them would be a repair.

Here it is becoming more common to run a dimpled membrane (like Delta MS or SuperSeal) from drain/footing to grade (or just above) .. sometimes in combination with a roll/brush on coating.

Some drainage issues can be simple to fix, some drainage issues are absolutely impossible to fix... the best you can hope for in a worst-case scenario is management (Installing a french drain, a sump pump, and a dehumidifier.)An extreme solution will involve re-grading the yard (sometimes this is possible, sometimes not), or excavating the basement wall(s) and installing waterproof membranes (AKA: plastic sheets), then filling up with a PROPERLY CONSTRUCTED french drain system (Most contractors wouldn't know a correct french drain if it bit them in the ***.)Good luck.

If it's a flat roof, there may be a chance that the insulation is on the top of the roof deck if you have a membrane or built up roofing systems.  

As Sergey said above, "Ice and Water" membrane are very important, especially in a place as wet as AL. 

If you make prudent use of acoustic sealant and/or hang a second layer of 1/2" drywall over the fire rated - with a liquid acoustic membrane (i.e.

Your best return money-wise is to jazz up the existing layouts as much as possible.While the floors have held up impressively, I'd still get down there, tap out the mosaic tile piece by piece, skimcoat with thinset, RedGard, and then tile over the membrane with thinset again. 

Metal can usually be repaired or recovered with a membrane.

And also, good thinking to have one account for 'receiving' money as almost a gate to pass the membrane into my bank account and then transfer it into another account that only I have the info for.

I have installed many types of flooring for basements but I would apply a water proofing membrane prior to installation of any floor.