Reconstruct under sampled signal
PWM is a non-linear process, and it contains rectangular pulses; in theory at least, it cannot be sampled without aliasing because its bandwidth is infinite. In practice, a sampling rate of 5 times the fundamental is enough in many applications; this would mean that you need a sampling rate of at least 25 kHz.

Once the signal is sampled, you can't eliminate aliasing by interpolating. The interpolated signal will still contain all aliases. In fact, it is in general impossible to eliminate aliasing once it occurs.

Even worse, the spectrum of the PWM signal is continuous, which means that the aliases will probably swamp the sideband at 60 Hz. In other words, your problem may have no solution.



EDIT: Would a narrow bandpass filter at 60 Hz work?

Short answer: I don't think it will, because there are likely to be aliases at 60 Hz; these will modify the amplitude and phase of the signal component at 60 Hz.

Longer answer: the spectrum of the undersampled signal is quite complex. First, the analog PWM process is non-linear, which introduces harmonics at multiples of  5 Khz. The actual shape of these harmonics is, I think, not trivial to calculate, but we can assume that they will include sinc-like spectra of very large bandwidth (since the PWM pulses can be very narrow). Adding to this the undersampling at 3.84 kHz, there will probably be complex aliasing happening at 60 Hz.

One thing you can do is look at the analog PWM signal in a spectrum analyzer. Set the tracing to "average" and let it run for a while. Find the bandwdith of each harmonic, and then see if any of them will alias at 60 Hz when undersampled. If (and only if) by a sheer strike of luck none of them do, then the narrow bandpass filter will work as you want.