Are birth control pills effective during your period?

I've been using the birth control pills on time for several months, we had unprotected sex during my period ( a day after it started), does the pill still protect me during these times?
Yes. Your pill is effective while on your period. It is extremely rare that a woman would become pregnant on her period regardless of birth control though seeing as a period happens when the egg is discarded from the womb.. you can't get pregnant if there's no egg to fertilize.
To Emry: You're very confused. The doctor calculates the date of conception if you're unsure two weeks after your period because that's generally when a woman ovulates.. not DURING her period!!

This can be normal for some women, while at the same time, this can be an indication of a problem for others. Each and evey women's body reacts to hormonal imbalance differently. May be your biological system take a little longer than others.
would recommend you to see your doctor and ask what he/she think about this. Since I do not have any data on your health history, I may not be able to give you a good answer. In short, this may be normal for you, but again, you need to ask your doc.
Yes... some women take longer like two or three months to get back to normal.

My ultimate advice is talk to your doctor and ask him/her. The way a lot of birth control pills work is to give a kind of mega-dose of hormones, these cause your body to not respond the same to sex (on a chemical level). They can also sometimes cause people's periods to either be super regular, or kind of hit and miss.
Also remember that pills are never 100% effective. As old fashioned as it may sound, the only sure fire 100% effective method of birth control is abstinence. I am not advising you not to have sex, I am just pointing out that you have to be careful if pregnancy is a concern.
My most important advice is this... NEVER have sex with any man that you would not want to make a father. Even if you are 100% positive that your birth control will work, don't take the chance. :P If you don't think he would be a good father, don't take the chance.
PS: This is an edit after the fact: This is in response to Olivia J's post. I have learned this from recent reading (I am going to be a father soon), but intercourse DURRING your period is when pregnancy is most likely to occure, especially towards the end of the period.
That fact suprised me as well. In fact if you are not sure of the date of conception, the doctor will guess two weeks after your last period.
Remember, conception doesn't generally take place the day of the act, it takes place a few days after. Also, your period is not simply the absense of a healthy egg, it is when the body is flushing the old one to put a new one in it's place.
I will agree that the pill is generally effective either way. However, do some research on the timing thing. You may be surprised.