Can one Enable Post-Mortem Debugging of Non-Cygwin Application Running in a Cygwin Terminal?

We have a system that's a mix of Cygwin and non-Cygwin programs, all of which run under a Cygwin bash session.

One of the non-Cygwin executables is periodically crashing, and I'm trying to enable post-mortem debugging using windbg as outlined here.

I wrote a test program that deliberately crashes. After following the steps in the above page, windbg opens up automatically when the test program crashes -exactly what I'm looking for. However, if I run the test program from Cygwin's bash, bash prints a "Segmentation fault" error message and windbg does not open.

Is there a way to get windbg to open up upon a non-Cygwin program, that was launched from a Cygwin bash shell, crashing?

P.S.: All of our non-Cygwin programs are C programs compiled with MS Visual Studio.