try wilcoxon test

Yes - I believe you can but I think you'd need a latent variable approach such as structural equation modelling. You model the couple's combination as a latent variable and probably the correlation between them and simultaneously a regression that predicts relationship from the other two variables.

Lots of great information dealing with couple's data at http://davidakenny.net/dyad.htm

Sounds like a very interesting study. A key determinant is what your unit of analysis is - whether it is the dyad (or coupling) or the partners as individuals. Also whether your analytic model assumes the partners are indistinguishable at the dyad level. The total N would need to be large enough to support SEM (not my area of expertise so can't offer guidance on sample size).

My understanding of attachment style measures is that the combination within the dyad could be treated as a single measure of the dyad (rather than as a pair of partner measures) as the combinations have conceptual standing. This would give 8 levels (assuming 4-type or 2-D anxiety/avoidance schemas). For SEM could keep to two original dimensions per participant unless you wanted to model the combination per se.

If for example, using  MAAS for mindfulness then you'd have a mean of a continuous measure for each partner which may be easier to keep as such rather than create a new "combination" measure that might be challenging to defend conceptually. It looks like studies of mindfulness and relationship satisfaction such as Barnes et al 2007 focussed on individuals and not partnerships as their unit of analysis.

Perceived relationship quality is conceptually very complex (e.g., Fletcher et al's PRQCI CFA model or Spanier's DAS) so the measure you'd use for this would matter in terms of the overall conceptual model underlying your study (e.g., relationship of say anxiety-avoidance style with trust aspect of relationship quality or dyadic-cohesion).

Best wishes for what sounds like an innovative and complex study!

Thank you all for such informative answers ( I use FFMQ created by Ruth A. Baer, ; PRQC created by Garth J. O. Fletcher and ASQ created by Judith A. Feeney) :)