It can be very difficult to compare statistical results from quantitative data with themes from qualitative data. This requires beginning your research with a careful design for your later analysis, so that you can write the data collection material for both studies in a way that will allow for an effective comparison.

Can I use inferential analysis with thematical analyses in a mixed-method approach?

You can do that but before applying those analyses, you need to structured your mixed method research design or choose the appropriate design that can address your research problem, meeting your research objectives & answering your research questions. After considering the design then you can adopt the relevant analyses to support the particular mixed method design. There are few designs within mixed method research - you can refer to this RG link below to know more:

https://www.researchgate.net/post/What_are_the_different_types_of_mixed_method_research_design

Muhammad - personally I would not advise undertaking mixed methods for an undergraduate degree. It would be more manageable to choose a single methodology. I assume that you mean using inferential stats for your quantitative component? You cannot use inferential techniques on qualitative data.

Agreed with Dr Dean that you can't use inferential techniques for qualitative data in which inferential techniques are for quantitative research whereas thematic analysis is for qualitative data.

Han Ping Fung Dean Whitehead I'm using inferential analysis for quantitative data acquired from questionnaires. Is that logical?

It can be very difficult to compare statistical results from quantitative data with themes from qualitative data. This requires beginning your research with a careful design for your later analysis, so that you can write the data collection material for both studies in a way that will allow for an effective comparison.

David L Morgan Does using pre-planned themes for the semi-structured interviews count as a careful design before the analysis? I've planned on using themes in my semi-structured interviews to avoid going off-course and to keep them similar to the questions in the questionnaire so that they are easily comparable later. However, at this stage, I'm more worried about this being academically logical than the actual difficulty of executing it. As I'm going to be marked for it as part of my research proposal module.

As David says, applying statistical methods of analysis to qualitative data can be problematic - however, if it is simply descriptive statistics (frequencies) - this is possible. But then you might want to re-think conducting interviews - if you want to know the frequency of something you can simply use a closed questionnaire (a structured interview would do the same job).

If you are talking about inferential statistics - again - unless you had a very large sample (usually not the case with interviews) - this is not advised.

I hope this helps.