Since mixed methods research is now such a widely accepted field, I don't think you need a "conceptual framework" for your methods. Instead, you need to develop a set of well-defined research questions, along with clear justifications for how your methods will address those questions.
You definitely can have a conceptual framework for the study as a whole, but it is not necessary for the methods section. Of course, if someone with power tells you have to, then it doesn't matter how inappropriate it is.
Instead, I would ask that person to recommend some examples -- preferably from published articles.