The internal conflicts for Macbeth, Lady Macbeth, and Banquo are as follows:
Macbeth struggles with his overwhelming sense of ambition, and throughout the play, he does not know how to go about attaining the status he desires. When the witches tell him that he will be the King of Scotland, he desires the throne so badly that he cannot wait for the situation to come his way naturally. So he struggles within himself over the right thing to do to achieve his goals.
Lady Macbeth's inner conflict revolves around her guilt at having set so many murderous deeds into play. She has persuaded Macbeth to murder King Duncan, but she never thought that this would lead to the murders of Banquo and Macduff's entire family. By the end of the play, Lady Macbeth is driven mad by her sense of guilt.
Finally, Banquo struggles with the knowledge that has been passed on to him by the witches. He has seen the prophecy come true for Macbeth, so he wonders whether or not it will come true for him.
In addition to the above, in Shakespeare's Macbeth, each of the characters has an additional internal conflict.
Banquo also struggles with his knowledge of what the witches told Macbeth. He knows what the witches predicted, so he suspects Macbeth of treachery. Yet, Macbeth is his friend and he has no proof. Banquo says when he opens Act 3:
Thou has it now--King, Cawdor, Glamis, all
As the Weird Women promised, and I fear
Thou played'st most foully for't.
Lady Macbeth, too, struggles with an additional inner conflict. When she pleads with the "spirits" to "unsex" her, etc. (Act 1.5), to make her more aggressive and pitiless like a man, she is actually revealing an inner conflict. As evil as she seems to be, she doubts her own ability to go through with the assassination. The fact that she feels the need to plead to be changed in order to kill Duncan, suggests that she actually doubts her own ability to do so. And, if fact, she can't go through with it. Even though she doubts her husband's ability to go through with the murder, when she has a chance to do it herself she cannot--the sleeping Duncan reminds her of her father: pretty sentimental for someone thought of as so evil, as Lady Macbeth often is.
Finally, Macbeth struggles with Duncan's humble nature and his fairness as a king (Act 1.7). At one point, he decides not to kill Duncan because of the kind of ruler Duncan has been. Of course, the threat of eternal damnation plays a part in his decision, too. Either way, however, Macbeth suffers from a specific inner conflict in Act 1.7.