It also depends what kind of music degree he wants, there can be a BA in music in which case he could major in music/jazz with a minor in whatever. You can also double degree, with a BM in Jazz performance and get a BA in something else. Some schools only offer a BM in performance (for example, I suspect but don’t know for certain that at USC or UCLA they may not offer a BA in music for performance, they may only have a BM). When they do offer a BA in performance, it generally has less of the theory and other classes a BM has,it is less ‘intensive’ (which may suit your son).
Elite schools like Columbia and the other ivies have strong music programs, but they don’t offer a performance degree at all, the BA they offer would be in theory, ethnomusicology, music history, etc), but they also strongly support music in the schools, so they have performance opportunities and with the Ivies I know of, they pay for lessons. Both Berklee and NEC have strong Jazz programs, so the joint program might be an option, but with those joint programs they are a very tough admit, that includes Juilliard/NEC (I think the Tufts one, if I remember what people have written on here, is a dual bachelors IE you get a BA from there, and a BM from the conservatory, others will comment).
In other words, there are a lot of options, and it will come down to your son and what he wants to do. If a program only has a BM, then he would need to do a dual degree from what I know if he wanted to do a non music related subject for a degree (my son is getting a BM from a conservatory and also is coming out with a minor in theory, but that is because they are both music related).