Multi Resolution STFT for audio
I've done multi-resolution spectrograms before, so they're not impossible (a unicorn).  One method is to zero-pad the shorter data window (for better time locality resolution) to the same length FFT as the longer data window (for greater frequency resolution).  Then you can simply scale for window length, and cross-fade the two sets of FFT magnitude results over some frequency range.  

Another possibility (instead of zero-padding) is to use interpolation of the lower frequency FFT or lower time resolution FFT results to create more possibilities for a higher density of spectrogram plot points.

One academic paper suggested computing the local vertical and horizontal contrasts at each spectrogram point and dynamically picking the FFT set with the highest contrast (over the vertical for narrow frequency spectra or across the horizontal for short time events) to plot at each point.

If you keep both (or more!) sets of (overlapped) STFTs, your transform isn't lossy, but redundant, and the resulting image can use that redundancy to obscure less information, usually due to graphical blurring/plotting with typical linear interpolation and/or non-linear color mapping.

Even for reconstruction you can use both sets of data, for instance feeding the short IFFTs to a tweeter and the longer IFFTs to a sub-woofer, with a cross-over in the middle (be careful of phase).