In TF2, how do resistances against dual-damage-type weapons work?

I ran some tests in MvM by giving myself resistance upgrades as a Pyro and letting flares hit me.

• No resistance: took 30 damage
• 75% fire resistance: took 7 damage (0.25x)
• 75% bullet resistance: took 7 damage (0.25x)
• Both: took 2 damage (resisted twice, [0.25*0.25]x)
• Extra damage from crit: 60 (regardless of resistance)

So, it appears that if a single hit is of multiple damage types, anything that modifies the damage of any of its types applies multiplicatively to the entire amount of damage. Crits are an additional package of damage of only the "crit" type, so resisting the base damage won't reduce the crit damage.

Applying this logic, a Sniper with the Darwin's Danger Shield (-15% bullet) and the Bushwacka (+20% fire) will take 1.02x damage from flares, taking 30.6 damage instead of 30 (big whoop).