well, (i think) the reason for this is that when water become wild (Wavy) it start hitting the seals at the bottom of the car and start pushing them hard, and sometimes open them - letting the water coming inside the car like anything.
now the issue with your car is that the foam inside the carpet is all soaked and smelly - now you have to remove, clean and dry it properly to finish this thing and also make sure while doing this you do put some silicon or other sticking glue on the seals so next time you might dont become the unfortunate one.
HONDA people are charging 6000 for complete cleaning service, but i would advise you to check with some good local denter / mechanic.