How does your institution credit a department's support of, and participation in, interdisciplinary programs?
Though this is not a full answer I did find one case documented in this paper[1] that may be of interest and that (I think) is worth quoting at length. It discusses the implementation of a 'Medical Biology' major at the University of South Dakota, which seems to essentially be a pre-Med degree. From what I gather, both the biology department as well as the medical school are actively involved in the major.

With regard to funding, the authors write:


  One other concern expressed regarding enrollments was that under the new RCM funding model adopted by the University, budget income from offered courses is distributed mainly to the college or school whose faculty members are teaching the course (100% if the major is in the same college or school), with a lesser amount (20%) being distributed to the college or school in which the major is housed, if that is different than the college or school offering the course. In the case of the Medical Biology major, which is housed in the Department of Biology, an increase in the number of required and elective courses offered by Medical School faculty members relative to a typical Biology major means that the College of Arts and Sciences receives less income from a Medical Biology major than from a typical Biology major. This concern was ameliorated somewhat by projections that the Medical Biology major would increase the overall number of majors in the Department of Biology, which it has, in fact, accomplished (see above), although administrative discussions about the most equitable distribution of funds from these courses is ongoing. (73)


The RCM model referenced is one in "which individual schools and colleges receive income based on student enrollments in their courses and must pay for other services provided by the university (mostly traditional administrative support centers)" (67).

So, in short, it does not seem that USD has found an extraordinarily innovative way to simultaneously support the two majors. However, the already-high demand for biology lessens the severity of this problem.

Unfortunately, I wasn't able to find any other papers that documented other cases of interdisciplinary major development.

[1] Goodman, Koster, Swanson. "The development and implementation of a new medical biology major including physiology," Advances in Physiology Education 39 (2015).