Hi There,
I've been taking oral birth control for about 10 years now, and just to ease your concern, breakthrough bleeding & brownish discharge are pretty common while your body is adjusting to any pill.
About 6 months ago, I switched to taking my pills for 84 days on, 7 days off. About 3 months in to the new method, I started spotting, but it was definately not regular blood; at first it was the thicker, brownish coloured discharge you were referring to. It lasted about a month! Since I stopped for 7 days and had my period, everthing has been fine. I also know that while your adjusting to your birth control (which can take up to six months, sometimes longer) missing your pill even by a few hours can bring on breakthrough bleeding, which is what happened to me.
I wouldn't worry too much about what you're experiencing, unless of course, you're having abdominal pain or the bleeding gets really heavy or has clots. Just continuing to take your pills on the same schedule will confuse your body less, and eventually you'll adjust.
If for some reason the discharge doesn't stop in the next week or two, go visit your Dr. Not all pills work for all people; maybe you'll just need to try a different kind. It took me a few years to find a pill that suited me, but since then, I've had no complaints.