Whatever the guy can do to elevate his heart rate would work for him- if he's overweight and not used to exercise, he MUST start slowly, build up a solid endurance base and increase his stamina before getting more into exercise. Don't go and push him because your exercise agenda is different than his. You are obviously both at different levels, and if you can't work within his schedule, better for you to give the moral support from the sidelines.
Having said that, if you did do the running, I think it would be an excellent way to cross train for your cycling. Running does use some different muscles, but the muscles you use for cycling that you also use for running will be used in different ways. I really do think this does help to increase the overall strength of your muscles, as long as you don't overdo it with the running.
It does sound like you and your friend have different agendas. Keep in mind, when someone decides to start exercising, they need support but not pushed to the point to where they hurt themselves, don't have fun with it, and can't keep up- all of these results will end up leading to the person quitting exercise due to discouragement, and that's the last thing you wanted to do since you're supposed to be the motivator, right?