Firstly, I would say it's a bit early yet to be jogging or running. With your limited ROM you might set yourself up for compensatory damages elsewhere. As your Ortho suggested, biking and swimming are good exercises to regain musculature and get cardio in. As you regain ROM, strength and balance, start slowly on the treadmill and gradually work up to backward walking, sidestepping, and ultimately jogging.
For your ROM. A good stretching plan should include iliopsoas and piriformis stretches. Straight leg raises in all planes. Also, with a theraband or theratubing, "steamboats" -sets of extension, flexion, adduction and abduction. With a belt or towel, hamstring and calf stretches.
This is a link for a knee rehab, but knee and hip (femur) rehab are very similar, so you might find this useful.
Dr. David Lintner - Orthopedic Sports Medicine Surgeon - Houston TX
Good luck.