It is absolutely possible to reach your goal by eating healthy and jogging. However, you must understand that losing the weight takes longer than putting it on. A good rate of fat loss is about 2 pounds per week.
Also, you are doing a lot of cardio, which is good, but make sure that you aren't cutting your caloric intake to much, or else you body might go into a "starvation mode" and start hording calories as fat. Try to get 5 smaller meals in a day, which will help keep your metabolism up throughout the day. And make sure that your are getting in a balanced diet, to include all the food groups... moderation is key.
I also recommend adding a resistance training program. Muscle needs more energy for it's general maintainance and survival than fat does so it will drive up your resting metabolism. If you're not looking to build size, then a muscular endurance training program is probably your best bet, as it will help condition you for your cardio regiment. You should get in at least one exercise per major muscle group a session (chest, back, shoulders, core, legs), at 2-3 sets for 13-18 reps with about 45-75 seconds rest between sets. If you don't have access to a gym then at least try to get some body weight exercises in (push ups, lunges, pull ups).
Best of luck!