Q: Is this a CP/M computer or an MS-DOS computer?
The answer to this question is "Yes." The Rainbow is both a fully functional CP/M - 80 version 2.2 and CP/M - 86 version 2.2 AND MS-DOS computer.
Due to its dual-processor design, the Rainbow has the ability to run both 8- and 16-bit programs. Its proprietary version of CP/M, CP/M - 86/80, can launch either type of program. The operating system was modified so that when a 8-bit program was executed, it would transfer control of the program to its Z80 CPU. In all other cases, it would use its 8088 CPU.
The Rainbow can also run MS-DOS. The most popular versions running on it were 2.05 and 2.11. Also available were 2.01 and, much later, 3.10b. All these versions of MS-DOS were modified by Digital to run on the Rainbow's hardware.
Three other operating systems were also available. Concurrent CP/M - 86 was produced for use on the Rainbow, but it could not run 8-bit programs. Venix, a UNIX-like OS, was supposedly compiled for use with the Rainbow, but has not turned up in years. Finally, UCSD p-System is also available.