Yoga can - among other things - improve your flexibility, for example, see this article in YogaJournal. The article argues that yoga both addresses the physical side of flexibility (muscle, ligaments, joints etc) and the neuro system part of flexibility.
My own experience of yoga is that is has helped me to be more flexible(for example, no problems with third world squat now, greatbig problems before), better balance (for example, no knee problems any longer when down hill skiing) and more aware of posture (less problems with my back).
To get started, find a yoga "dojo" that fits your style/perspective and take some classes regularly for a few months. For me, I liked the ones that focus on the physical side better than the ones focusing on the spiritual side.
Yoga is then quite easy to integrate in daily training routines and also a way of "going to gym" training that is easy to bring your spouse too.
For example, you could do a short yoga routine as a warmupwarm-up for both your Body weight routing and your Running routine.