No, not quite. The macOS/iOS kernel is extremely Frankenstein-y (not meant in a derogatory way), with the majority of codebase being extremely Apple-specific, and bits and pieces originally taken from Mach and BSD. In particular, there is no microkernel, and there never was. Mach itself was never used as a true microkernel in a commercial setting, with the first such implementation--Mach 3--showing significant real-life performance problems. As such, there is no "BSD on top of a Mach microkernel". It is and has always been a fully monolithic kernel with some subsystems originally derived from Mach (Open Group's Mk 7.3), some from BSD (FreeBSD 5), and the rest developed in-house over the years. Even the layerings aren't always clean, with "on top of" often morphing into "alongside" or "intertwined with".
What is interesting about Mach to me. Is that now 40 years later it's returning too it's roots of hosting multiple OS's on a single hardware architecture. Apple being able to design to M series chips to match Mach's paper over Mach's deficiencies and leverage it's strength I find very exciting.
Originally it was meant to be the foundation computing layer for a campus full of devices.
