If you're a veteran who has used post 9/11 GI Bill...

If you get BAH in online classes you'd prob still qualify in the summer but the rates may be much lower since you are taking fewer hours. If you only take 3hrs you are not going to get the same rate as if you were taking 12hours. Try www.va.gov. They should have a link to the GI Bill website. I'm pretty sure there's a chart that caculates the rates of BAH based on hours and type of schooling. If you need the same rate of BAH to pay the bills during summer semester, you may have to just go ahead and take the same amount of hours you were taking before if they don't have a fixed rate for summer.

Do I get BAH while enrolled in distance learning?Answer
Those enrolled solely in distance or online training will be entitled to 1/2 the national average BAH rate of $1,346.88 monthly (or $673.44 monthly). On August 1, 2011 these rates will change to $1,368.00 monthly and $684.00 monthly.
According to site yes you will get BAh if you are enrolled full time but if semester starts on june 15th you'll only get half of the month's pay.