Hi, 

The basic source on this question would be Creswell's book on mixed-methods:

Creswell, John W., and Vicki L. Plano Clark. "Designing and conducting mixed methods research." (2007).

In practice the terms qualitative and quantitative research turn out to be quite versatile and, as such, not strongly linked to a particular research philosophy. In other words, most research philosophies have their own preferences on how to do qualitative and quantitative research. This is somewhat problematic. See for example Bergman’s introduction in: 

Bergman, Manfred Max, ed. Advances in mixed methods research: Theories and applications. Sage, 2008.

Our own take on this problem is to surpass the quant/qual dichotomy and build a mixed method methodology from a taxonomy of research methods that is more coherent in terms of ontology, epistemology and axiology. (paper attached).

My2Cents, 

Conference Paper Design Patterns for Mixed-Method Research in HCI

Koen, I agree that qualitative, quantitative, and mixed methods research can all be done from a variety of different philosophical perspectives. I would add that you don't have to choose one perspective and use that exclusively in your research; you can use ideas from different perspectives in your work. See the attached paper.

I would strongly suggest looking at Crotty  (1998), the start of chapter 1, page 6. In my view this is the clearest explanation there is on how to determine the links between epistemology,  theoretical  perspective, methodology and methods for qualitative and quantitative research.  It provides tables to work this out and an example of a flow diagram to present it.

W

The main problem with Crotty's book (The Foundations of Social Research), aside from its being almost 20 years old, is that it doesn't deal with either realism or pragmatism as distinct approaches, quite different from positivism, constructivism, etc. Both of these are important stances in contemporary social research. For realism, see the attached paper; for pragmatism, there are several discussions in the two editions of the Handbook of Mixed Methods (Tashakkori and Teddlie, eds.)..