I work across disciplines including geology, biology, and chemistry. I currently collaborate with atmospheric chemists, on a manuscript primarily geared for microbial ecologists.
As a first general strategy, if you can find an example of another scholar blending the two fields you're interested in, you can do something like: "Using the rationale of xxx, we yyy (citation)."
As a second general strategy, some groups gloss over the secondary discipline and focus on the primary discipline. This approach is also used in the choice of journal that you plan to submit to. (If it is for your thesis, you can go into more depth on both disciplines - your committee's job is to assess you and you should try to be more thorough.)
As a third general strategy, I would look for examples in the fields you are trying to merge.
- Go to google scholar
- Emter discrete search terms for the two fields. In my case it would be microbial and stratospheric, or something similar.
- I might limit the results to the last five years since much of the 20th century was different (and comp bio was new then anyway).
- Read through a few. Get a feel for how other authors blend them. I did this as an exercise within my own fields just now to make sure the advice is sound, and it seems that in general - strategy 2 above is favored. For example, the link describes a study blending classic microbiology and astronomy, which is 'really cool' for origin-of-life implications.
- Distill a template from what others have done. Don't try to reinvent the wheel - :) - as you are not doing as evidenced by your question here.
I don't know if these ideas will be helpful. I always find example papers to provide good working mental templates. And, don't underestimate the flexibility that referencing others' work gives us.