A few years back, I wrote some util library around DShow/DSound to let me play MP3s in a Windows C++ application. Is that still the normal way to do it in a C++/MFC app, or
Youc could use MCI windows functions, https://msdn.microsoft.com/en-us/library/ms709626
It can play many of audio file formats including MP3, WAV, MIDI etc.
If I recall correctly it does not require DirectX.
The PlaySound function might also work for you.