inverted input for adc
You say your input signal has 1.5 V DC bias, and that you have chosen a reference voltage of 1.5 V.  Connect the - input to this reference, and the + input to your signal and all should be fine.

Basically, it appears that this A/D always converts the difference between the inputs.  If you don't actually have a differential signal, then set the - input to the fixed midpoint voltage of the single-ended signal.