The Darwin portion is for most intents and purposes based on BSD -- particularly FreeBSD-- running on top of XNU (a hybrid Mach 3.0 microkernel with big chunks of the monolithic BSD kernel embedded).
http://en.wikipedia.org/wiki/Darwin_(operating_system)#Kerne...
Concerning the BSD portions, see this from Apple's Kernel docs: http://goo.gl/1sp69
"Integrated with Darwin is a customized version of the Berkeley Software Distribution (BSD) operating system. Darwin’s implementation of BSD includes much of the POSIX API, which higher-level apps can also use to implement basic app features. BSD serves as the basis for the file systems and networking facilities of OS X. In addition, it provides several programming interfaces and services, including: The process model (process IDs, signals, and so on); Basic security policies such as file permissions and user and group IDs; Threading support (POSIX threads); Networking support (BSD sockets)"
That accounts for an immense amount of what a kernel normally does.
Besides, I have never met a NeXT or Apple employee that didn't consider Darwin to be BSD.
It's a radically modified BSD but I think it's still a descendant.