What kind of design are you using -- for instance convergence or explanatory sequential? Either way, if you have hypotheses for your quantitative study, then interpretivism would not be a good fit for that part of your project.
Hi. Your question is very general. In order to answer it more precisely, it would be important - even if as a heuristic - to know more about the projected research design.
Basically, 'interpretivism' is a more qualitative approach to social research. Interpretivists believe that individuals are complex people. That is, individuals perceive 'the same reality' in different ways and they behave differently. This point of view has epistemological and scientific consequences, because interpretivists more or less insist on the point of view that 'scientific methods' are not really suitable to document, analyze or interpret human behavior.
In methodological terms, it is important to note: Interpretivism recommends primarily qualitative research methods (especially participant observation and unstructured interviews) to analyze social behavior. In documenting, analyzing, and interpreting the data obtained, interpretivism must take into account the fact that human knowledge about the world is socially constructed. For interpretivists, knowledge is not objective or value-free, but is produced and transmitted through discourse, ideas, and experience.
As a result, one must use appropriate scientific concepts and operational methods to relate and evaluate these discourses, ideas, and experiences in such a way that the study design does not contradict the preliminaries of interpretivism. The epistemic and epistemological problems involved on the one hand, and the methodological and operational requirements on the other, are anything but trivial. Great caution and care are required.
The standard philosophical paradigm associated with mixed methods research is pragmatism, which is pluralistic and focused on what works best to address the problem under investigation. You might consider the following for further germane insights.
Alise, M. A., & Teddlie, C. (2010). A continuation of the paradigm wars? Prevalence rates of methodological approaches across the social/behavioral sciences. Journal of Mixed Methods Research, 4(2), 103–126. https://doi.org/10.1177/1558689809360805
Allmark, P., & Machaczek, K. (2018). Realism and pragmatism in a mixed methods study. Journal of Advanced Nursing, 74(6), 1301–1309. https://doi.org/10.1111/jan.13523
Creswell, J. W. (2022). A concise introduction to mixed methods research (2nd ed.). https://us.sagepub.com/hi/cab/a-concise-introduction-to-mixed-methods-research/book266037
Kaushik, V., & Walsh, C. A. (2019). Pragmatism as a research paradigm and its implications for social work research. Social Sciences, 8(9), 255. https://doi.org/10.3390/socsci8090255
Molina-Azorin, J. F., & Fetters, M. D. (2022). Books on mixed methods research: A window on the growth in number and diversity. Journal of Mixed Methods Research, 16(1), 8–16. https://doi.org/10.1177/15586898211068208