AD623 use case

Hey everyone,

I just want to check whether im using the ad623 in a way which it'll work.

I have two connected, both single supply with 0 and 3.3V. The gain resistor is set to 381 and the power supply has a 10uF capacitor  as well as a 100 nF.

I have it set up so that when a positive voltage appears across the input the one ad623 should output the differential voltage * gain and the other 0V.

If a negative voltage appears across the terminals it should do the reverse where the other ad623 outputs the differential voltage * gain and the other 0V.

So in other words the +In  and - in of each one is the inverse. The reference pin is tied to 0V.

When applying a small 1mV signal both seem to output positive voltages although the one ad623 should see 1mV and the other -1mV.

Anything I'm incorrectly applying?

Any help will be appreciated