Is capacitance inversely proportional to voltage?

In a word, no.

The of a device is equal to the charge stored on the device divided by the voltage applied to the device. So it might seem that capacitance is inversely proportional to voltage. However, capacitance is independent of both charge and voltage. Capacitance is determined entirely by geometric factors and the dielectric constant of the space between the conducting places that form the capacitor.

So while capacitance is defined to be the ratio of charge to voltage for a capacitative device (a capacitor), it is somewhat misleading to say that capacitance is inversely proportional to voltage. If I double the voltage applied to a given capacitor, I won't halve it's capacitance. I'll simply double the stored charge on the device.