You certainly could use interpetivism for the qualitative portion of your mixed methods study, but it is not likely to be a good first with survey analysis.
For mixed methods, the most important question is how you plan to integrate the findings from your qualitative and quantitative methods.
Yes, interpretivism can be adopted in the textual analysis and semi-structured interviews and can be used for corroborating the findings of the survey method.
Interpretivism is certainly the only option for the qualitative aspect of the mixed method. I am just wondering a bit how effectively you will be able to use same for the survey portion which is most likely to be quantitative and demands positivism approach in analysing the data.
Directly comparing the results of qualitative and quantitative methods is only one of many possible designs in Mixed Methods Research. In particular, that design is often known as convergence (or in its older form, triangulation). Generally speaking, the point of that design is to determine if the two sets of results agree ("converge"), which would lead to a cross-validation, indicating the results were probably not due to the method being used to produce.
In contrast, two other very common designs are "exploratory sequential" (qual --> QUANT) and "explanatory sequential" (QUANT --> qual). The first of these uses preliminary qualitative methods to develop the content and procedures for a subsequent quantitative studies. The second follows up on a quantitative study to better understand the nature of the results.
These three designs are not the only possibilities in Mixed Methods Research, but they probably are the most frequently used designs.