I got a Bachelor's degree in Electrical Engineering, followed by a Master's in Computer Science. Actually I don't consider them unrelated, as I have found lots of jobs (I'm a consultant/contract programmer) working on embedded systems -- either doing both the hardware and the firmware design, or just one or the other with a good knowledge of the entire system.
My combination of a BSEE and MSCS degree has directly gotten my contracts -- my clients have told me so.
Likewise, I don't see that a BS in Civil Engineering and an MS in Computer Science are unrelated, due to the heavy use of computers in the civil engineering field today. I would definitely go with the mixed degrees.
As far as "selling" the mixed degrees vs the BS/MS in one field, generally pursing an advanced degree in the same field would lead one to some degree of specialization, and unless the employer just happens to be looking for that specialization, the extra education is not of much benefit.
Where with the mixed degrees, I was able to do a thesis on a topic that involved both hardware and software and demonstrated knowledge of both fields. So I believe your friend would be wise to consider a MS thesis along similar lines, which would combine his newly acquired computer science knowledge with his undergraduate training.