Could Delayed Periods Be Normal While On Contraceptive Pills?

Hello i m 23yrs old and is it normal to miss a period on the Alesse birth control? I started taking them May 16th the first day of my last cycle.. I took them every day at the same time.. I didnt get a period the whole june but i started my period on June 30... also when do i start my new pack now on my period or after?