Housework does not count toward "me" time unless it is cathartic or emotionally balancing for you in some way. And even then, I don't think it should count unless you want it to.
Do not give up your running time. Tell DH that your "me" time is when you are free of responsibilities, to do what you wish. So, housework doesn't count, neither does the commute, since you have to work. And if need be, sit down and show him a chart of the hours during the week when he is doing his own thing (socializing with friends, watching TV, playing on the computer, reading the paper), vs. your "me" time (20 min of running).
Then, tell him that you want to be appreciated for the work you do, and shown consideration for it by having a spouse who allows you time to refresh yourself and follow your own hobbies, instead of a spouse that focuses only on what he thinks you're getting and he's not (antogonism vs. cooperation). And then tell him that you will put in a greater effort to show him your appreciation of his hard work, since that might be what the problem is (you can say it, even if that's not what it is, because it might be contributing). Then, thank him for working at his job for the benefit of the family. Thank him whenever he helps around the house, or drops off the baby at daycare, or does the grocery shopping. And after a few weeks of this, schedule some me time for yourself, and let him know that him generously watching the baby (without grumbling or making it a tit-for-tat) while you recharge/refresh/do your own thing is one of the best ways he can thank you for all your hard work. And say it with a smile.
To answer your question, I get about 20 minutes of me-time per day, if I give up some sleep to do it. And 1 hour on the weekends, for a tai-chi class.