using Atmega328p and its ADC to read both negative and positive values
What you're looking for is AC-coupling.

Since you don't care about the DC-content of your signal, you can simply use a capacitor to transfer the signal to any other voltage level, as for example provided by a voltage divider bias:







simulate this circuit &ndash; Schematic created using CircuitLab

This will place the ADC input in the middle of the ADC range if there's no external signal present, and will make it oscillate around that if there is external signal. The values of C1 and R1, R2 depend on the frequencies you want to let through, and how the sensor is driving its signal output – what you're building here is effectively a RC-highpass filter.