Your benefits start the first of the month following the month of your employment. Meaning, classes usually start mid to end of the month. You will get coverage the following month. Pretty good deal. Not a lot of time without coverage. Remember that you can sign up for cobra within 30 days of your resignation date from your previous job. ( I believe it is 30, might be longer) I had this in my back pocket for the 5 days my family was uninsured. That way if someone needed the doc in that short time, I would just immediately sign up for cobra. Luckily we didn't and everything worked out.
What info do you want on family bennies for travel? Immediate family and one set of parents get them. Plus buddy passes. ( I think 24-28 of them.) if I remember right, it comes available 30 days after doh. But be careful.... Our flights are really full. These new seat con figs seem to be allowing more non-revs on though right now with the higher seating copacity. From what I have seen.
Hope that helps, I may be a little off on my effective dates on the non- rev, but I think that is correct.