I have NOT read all the responses here but after skimming just the first page I was ALARMED by the number of responses where people said to loosen the reigns, let them run free, they will be fine.
I am the FURTHEST thing from being an overprotective parent and I do give my child lots of freedom, but NOT at the pool. He runs rampant at our local park (sometimes out of my sight) and he is afforded other freedoms as well.
I was a lifeguard for 13 years. My best friend helped provide CPR to a 6 year old little boy who subsequently died. He was wearing a flotation device (back float, not a life jacket) and was found floating face down in the water. The parents sued the facility and the case went to trial. My best friend had to relive that experience over and over (through depositions and testifying). The ultimate result was that the facility was not at fault. DUH! If anything it is my opinion that the parents were negligent. They sent their child to a "kids night out" pool party KNOWING their child was not a strong swimmer (thus why he was wearing a flotation device). The facility administered swim tests to all children attending the party and he was determined to be a weak swimmer, therefore he was wearing a float and restricted to shallow water. FYI...he drowned in 3 feet of water...where he could touch.
The other story I must share is one that happened in the city where I live just a couple weeks ago. A family was swimming at a country club. Again...it was a 6 year old boy that was swimming. He was a strong swimmer and was going down for dive sticks. The mother was watching him. She turned around to lift a lounge chair and when she focused her eyes back to where her son had been swimming (a mere 10-20 seconds later) she didn't see him. He was found at the bottom of the pool, given CPR, taken to the local children's hospital and was taken off of life support the next day and died.
My point is this...whether a child is a weak swimmer as in my first story or a strong swimmer diving to the bottom it doesn't matter. A child (or anyone for that matter) can drown in very little water. No matter how strong of a swimmer my child is/becomes he will be watched ALL THE TIME while at a pool. I don't take my eyes off of him for even a second. Right now he is 4 years old and that means if he wants to swim that I must as well. he does not enter the pool before me...even in a 18inch deep "baby pool". I sit in the pool while he plays. There will come a time where I watch from the side but he will have my undivided attention...no reading books or partaking in otherwise distracting behavior. Many children drown each year with multiple adults "watching them" because al the adults assume the other is watching the children.
OK...sorry for the rant and ramble. I will get off my soapbox now!

This just hits very close to home for me so I couldn't NOT reply!
ETA: To the OP...if you are still reading, please share these stories with your DH and hopefully this will help convince him that a pool is NO place to be lax!