Martyred means to witness, it does not mean to suffer, it means to witness suffering and to know that it is wrong and yet it is happening. In the face of suffering there are only two alternatives to being a martyr: (1) to be blind to your own feelings, to be numb - to avoid, gloss over, or madly distract yourself from the suffering (e.g., with drugs, alcohol, television, sex, etc.). Although you may succeed to some level, you make yourself dead inside. The other alternative is to (2) live your life based on the suffering, to believe in the suffering. This will make you feel hopeless and depressed. In the first case there is a failure to accept that suffering exists. In the second case there is a failure to accept that suffering is transient, that it has a cause and that it will pass when the conditions that cause it have passed. Also, that there are things we can do to cause those conditions to pass.
The first step is to witness the suffering and accept its existence. This is martyrdom. Most Christians believe that martyrdom means to die or to suffer for your beliefs. This is wrong. In the bible the martyrs were persecuted and killed for their beliefs but the actual act of martyrdom occurred in the way they accepted their situation and the consequence of their decision. Also, it is important to understand that martyrdom is not about passively accepting suffering. It is about accepting the current situation and choosing to act compassionately. The martyrs in the bible chose to die to support the early christian church, which taught compassion within a brutal empire, and brought great benefits to the poor. Of course the ultimate expression of this in Christianity is the martyrdom of Jesus (God) on the cross.
The battle that goes on inside yourself is called noetic warfare by Christian mystics. This battle exists because suffering exists. It is a condition of our existence. In Buddhism, this fact is known as the first noble truth. However, many Buddhists skip over the first noble truth - of course suffering exists, that's why I'm a Buddhist, I want to move on and get rid of suffering. But, like the other noble truths, the first truth is not just a fact, it is an ongoing action, and it is arguably the hardest of all the noble truths. The first noble truth is the last noble truth because all actions in Buddhism are ultimately focused on dealing with this truth, that there is suffering.
This, I think, is why Buddhism and Christianity should be studied together, because of all the world religions, they are two that are most directly focused around suffering.