If this is a typical case of a podcast that sounds like a radio broadcast then you could discriminate between music and speech purely based on the "shape" of the spectrum.
I am not sure if there is special software that could handle this but I will provide a simple example using Audacity further below.
The main idea is that a mixed track coming from a variety of different instruments would be expected to occupy a wider range of the spectrum than just someone talking.
Here is a quick test using Audacity:
Just by visual inspection, a set of "noisy bands" appear in the spectrum view. These are the locations where it is either music played along with someone speaking or just music playing.
My settings for this image (Edit->Preferences->Spectrogram): Window-size 4096, window:Blackman, minFreq:0, maxFreq:8kHz, Gain:20, Range:80, freqGain:0, use grayscale.
To switch to this view, load your podcast into Audacity and then click on its track name and select "Spectrogram".
To achieve the same thing in an automatic way, you would have to create a very simple classifier. The classifier would break down the incoming signal into "chunks" and obtain their spectrum. This is roughly what Audacity does to generate each one of the vertical columns that make up the spectrogram of the sound. The classifier would then "scan" these columns from left to right deciding what each column represents ("Music", "Speech", ..., other?). The decision would be based on the relative amplitude of each harmonic in the spectrum. After this, you could decide to drop or silence those frames that have been characterised as "Music".
But all this means writing some form of code in a programming language (e.g. Python). I can expand this response with the simplest of classifiers that could work for this problem but only if that would be seen as useful (?).
Of course, this technique would work with mixed tracks whose full spectrum (including all their possible harmonics) extends well beyond the spectrum of the human voice. There might indeed be some special cases as mentioned earlier by
robert bristow-johnson where the discrimination is much more difficult and more complex techniques would be required but for a generic podcast, just basing the decision on the spectrum might do just fine.
By the way, the podcast I used in this example is this one.