Alas, you are trying to get a DC signal out of an audio jack. i.e., Your audio jack is AC, with an average DC value of zero volts. (You might even find that your audio driver feeds the signal to the audio jack through a capacitor...) So, you need to choose a way to convey your information on an audio signal. This can be accomplished by using some means of modulation. You could use amplitude modulation or frequency modulation quite easily. You will of course need to demodulate the signal after it comes out of the audio jack, and before it gets to your H-driver. I'm not sure how you are creating the audio signal that is to come out of your audio jack, but that may determine whether you use AM or FM. If you use AM, you could simply use a signal that is either on, or off, at any instant. (Similar to what is used when sending Morse code on an RF carrier.) Then, if it is on 50% of the time, assume this is zero drive. If it is on more than 50% duty cycle, then translate that to a positive pulse width that is proportional to the amount it is over the 50%. Conversely, to drive negative, simply force the signal modulation period to be less than 50%, and assume this is a negative drive... Quite simple actually...
If you want to go FM modulation, which will work just as well, you can pick a center frequency, say 10 KHz, and assume that it is the no-drive frequency. And, any frequency above 10 KHz can be interpreted as a positive drive, and any signal below 10 KHz can be interpreted as a negative drive. And, the deviation in frequency from the 10 KHz can determine the PWM percentage in each direction...
Be sure to have a dead zone on your demodulator, for either AM or FM, as you may not have exact control of the signal generation... Plus, it is a good design practice... And of course, be sure to accommodate the situation where you have no signal. i.e., your demodulator must interpret the lack of signal as a "No-Drive" command...