Ahh, the problem is the pills. They are hormones. Stopping and starting them can really screw up your cycle.
Some women do have breakthru bleeding when taking birth control pills. If you see your doctor, s/he can change your prescription if this is bothersome to you.
It isn't advised to quit birth control pills in the middle of a cycle since it can throw your period/cycle out of it's 'normal' sync.
Good luck!