Kenmore water filters make my water taste bad

I have an 11 year old Kenmore side-by-side and this past September my refrigerator started smelling like old lettuce - it was vile! It affected the freezer as well as making the water taste bad. I've gotten the smell to go away but the water still tastes horrible. I've replaced two filters and it's still nasty tasting. I've flushed gallons of water through it and still no change. If I remove the filters, the water tastes normal. I know they've changed the filters for this model and I'm wondering if I have gotten defective filters. I have had two repairmen out and neither could find a problem!