This is a recurring question I have heard people ask for many years.

While I believe traditional cross training is very effective, in my opinion, it's better to separate cardiovascular workouts (like running) from strength training workouts (like heavy weight lifting). With the exception of a moderate warm-up run, it's usually best to avoid doing both during the same workout. Instead, space them out. For example, try doing one workout in the morning and the other at night.

Note, if your primary goal is building muscle mass (through weight lifting), you may want to minimize the distances that you run. Likewise, if you're training for a road race (or competition), try using lighter weight and doing more repetitions when weight training. This will prevent them from working against each other and improve your overall training.