It looks like your water district might have added Free Chlorine (FC) to the supply, but along the way it got converted to Combined Chlorine (CC) possibly from organics along the way. However, when our water district used chlorine, I didn't see that effect and had FC of around 1 ppm and no CC (<= 0.2 ppm). Did you test your tap water using a 25 ml sample so you could get 0.2 ppm resolution? It may be that the FC is actually very low, perhaps <= 0.2, which would mean that you water district is likely using monochloramine at around 1.5 ppm. My water district now uses monochloramine at around 1 ppm CC.
Ah, no I used the smaller 10ml sample. I'll retest tonight with the 25ml sample.
Monochloramine is intentionally used because it does not form as many disinfection by-products and also persists longer in the water lines. It's also less reactive than chlorine, but that's a good thing in this case and is still strong enough to prevent runaway bacterial growth in the water (though not as fast as chlorine for person-to-person transmission, but we're talking water in pipes, not pools).
I certainly hope this is the case in my water district as well, because the alternative is disturbing.
Standard activated carbon water filters will remove both chlorine and monochloramine which explains your refrigerator water filter result.
Richard