High pass filter is not resulting as good as the scope's AC coupling
Either your capacitor has some leakage so it causes a bias in the output voltage:







simulate this circuit &ndash; Schematic created using CircuitLab

Or whatever you are connecting it to has some nA of bias current, or both. 

The offset is dependent on the ratio of the leakage to the load resistor in the first case. If you are using an electrolytic capacitor you could change to a low-leakage type or to a film or ceramic type. Increasing the value of C1, if it remains an electrolytic, will not necessarily help because the leakage tends to increase with capacitance for the same type of electrolytic cap. 

Edit: 







simulate this circuit