This text is written from a personal perspective and I'm not sure how well it applies to other scientists. If you agree or disagree please let me know.
A standard tenet of experimental science is that the number of parameters that one varies in an experimental set-up should be kept to a minimum. This makes is possible to disentangle the effects of different variables on the outcome of the experiment. It has been claimed that the pace at which physics has moved forward in the last century (and molecular biology in the last half century) is due to possibility of physicists to isolate phenomena in strict experimental set-ups. In such a setting each variable can be varied individually, while all others are kept constant. This is in stark contrast to e.g. sociology, where controlled experiments are much harder to perform.
In a sense the process of doing science is similar to an experiment with a number of parameters. The 'experiment' corresponds to a specific scientific question and the 'parameters' correspond to different approaches to solving the problem. However, we do not know which approach will be successful. If not, it would not classify as research.
Most approaches or methods are in fact aggregates of many submethods. To give an example, say that I would like to describe some biological system using ordinary differential equations. Then the equations I write down might be novel, but I rely on established methods for solving these equations. I try to describe the system by trying (varying) the equations that describe the dynamics until I find the ones I'm happy with. In this sense we use both existing and new methods when trying to solve some scientific question. However, in order to actually make progress we often minimise the number of novel methods in our approach. If possible we only vary one method and keep all others fixed.
The problem with interdisciplinary research is that it often calls for novelty on the part of all the involved disciplines. In the case of mathematical biology for example we are asked to invent new mathematics at the same time as we discover new biology. Maybe this is not always the case, but to a certain extent these expectations are always present. A mathematician is expected to develop new mathematical tools, while a biologist is expected to discover new things about biology.
If both parts enter a project with the ambition of advancing their own discipline this might introduce too much uncertainty in the scientific work (we are now varying two "parameters" in the experiment), which could lead to little or no progress. If the mathematician stands back then new biology can be discovered using existing mathematical tools, while existing biological knowledge and data could serve as a testing ground for novel mathematics.
So what is the solution to this problem? I'm not sure. But being clear about your intentions in an interdisciplinary project is a good starting point. And maybe taking turns when it comes to novelty with an established collaborator.