Learned this the hard way.
Beginning athletes have poor energy partitioning- you can train aerobic or anaerobic, but not both at the same time.
Strength training and running both use a lot of the same neuro-muscular systems and its really easy to have them both leech your recovery ability.
If you have exceptional genetics, you can handle both, but most people are just better off picking one (GET HUGEGETHUGEGETHUGE) and ignoring the other.
I stopped doing HIIT between my lifting days and my lifts shot up. Better energy, better recovery- just a completely different universe.